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Fractionally integrated APARCH modelling of stock market volatility: A multi-country study
Abstract
Tse (1998) proposes a model which combines the fractionally integrated GARCH formulation of Baillie, Bollerslev and Mikkelsen (1996) with the asymmetric power ARCH specification of Ding, Granger and Engle (1993). This paper analyzes the applicability of a multivariate constant conditional correlation version of the model to national stock market returns for eight countries. We find this multivariate specification to be generally applicable once power, leverage and long-memory effects are taken into consideration. In addition, we find that both the optimal fractional differencing parameter and power transformation are remarkably similar across countries. Out-of-sample evidence for the superior forecasting ability of the multivariate FIAPARCH framework is provided in terms of forecast error statistics and tests for equal forecast accuracy of the various models.
... We also use the FIAGARCH model with Student's t-distribution to compare the time varying correlations of the two methods. The main features of the bivariate FIAPARCH framework allow one to consider long memory, asymmetries and fat-tails as main stylized facts in the univariate CDS spread volatility (see, among others, Conrad, Karanasos, and Zeng 2011), which are also pertinent to the analysis of CDSs. ...
... Formally, the FIAPARCH model reduces to the FIGARCH model when δ = 2 and γ = 0, while it becomes an APARCH model when d = 0. Given our objective in this section, the DCC-FIAPARCH model, which measures a multivariate dynamic conditional correlation FIAPARCH model, combines the FIAPARCH and the DCC processes of Tse and Tsui (2002). Conrad, Karanasos, and Zeng (2011) has analysed the applicability of the multivariate constant conditional correlation (CCC) version of this model and finds that it is generally applicable when the financial time series exhibit power, leverage and long-memory effects, which is the case in our study (Lahiani, Hammoudeh, and Gupta 2014). The multivariate conditional variance-covariance matrix is given by ...
... Our main purpose is to take into account the presence of fat tails in the CDSs price changes. In fact, it is well recognized that the Student's t-distribution is more suitable for modelling the fail tails in financial time series than the Gaussian distribution (see, among others, Conrad, Karanasos and Zeng 2011). ...
The main purpose of this article is to analyse the co-movement in both time and frequency between financial sector CDS indexes and between these indexes and their main economic and financial control variables for the period 2004–2014. Empirically, we implement the wavelet-squared coherence methodology to analyse the co-movement through time, frequency and power. Our results unveil that the co-movement between the three financial sectors’ CDSs changes through time and investment horizons, stressing the importance of hedging portfolios in real time. Also, we uncover that the changes in co-movement to relatively higher frequencies coincide with the inception of the recent global financial crisis. This result is collaborated with the co-movement between each CDS index and other global risk factors, including crude oil prices, interest rates and equity market volatility. Finally, we compare the wavelet coherence results with those of the DCC-FIAPARCH model and find that the two different approaches provide quite similar conditional correlations over time. Our results are important for investors, debtors, creditors and other decision-makers which are interested in CDS spread co-movements at different frequencies or investment horizons. It would be useful for all market participants to resort to an appropriate frequency domain to have better understanding of the sector CDS interrelationship behaviour in this domain.
... To capture the contagion behavior over time, we use a multivariate fractionally integrated asymmetric power autoregressive conditional heteroskedasticity (FIAPARCH) framework, which provides the tools to understand how financial volatilities move together over time and across markets. Conrad, Karanasos, and Zeng (2011) applied a multivariate FIAPARCH model that combines long memory, power transformations of the conditional variances, and leverage effects with constant conditional correlations (CCCs) on eight national stock market indices returns. The long-range volatility dependence, the power transformation of returns, and the asymmetric response of volatility to positive and negative shocks are three features that improve the modeling of the volatility process of asset returns. ...
... The FIAPARCH model increases the flexibility of the conditional variance specification by allowing an asymmetric response of volatility to positive and negative shocks and long-range volatility dependence. In addition, it allows the data to determine the power of stock returns for which the predictable structure in the volatility pattern is the strongest (Conrad et al., 2011). Although many studies use various multivariate GARCH models in order to estimate DCCs among markets during financial crises (Celık, 2012;Chiang, Jeon, & Li, 2007;Kenourgios, Samitas, & Paltalidis, 2011), the forecasting superiority of FIAPARCH on other GARCH models is supported by Conrad et al. (2011) and Chkili, Aloui, and Nguyen (2012). ...
... In addition, it allows the data to determine the power of stock returns for which the predictable structure in the volatility pattern is the strongest (Conrad et al., 2011). Although many studies use various multivariate GARCH models in order to estimate DCCs among markets during financial crises (Celık, 2012;Chiang, Jeon, & Li, 2007;Kenourgios, Samitas, & Paltalidis, 2011), the forecasting superiority of FIAPARCH on other GARCH models is supported by Conrad et al. (2011) and Chkili, Aloui, and Nguyen (2012). ...
The aim of this article is to examine how the dynamics of correlations between two emerging countries (Brazil and Mexico) and the US evolved from January 2003 to December 2013. The main contribution of this study is to explore whether the plunging stock market in the US, in the aftermath of global financial crisis (2007–2009), exerts contagion effects on emerging stock markets. To this end, we rely on a multivariate fractionally integrated asymmetric power autoregressive conditional heteroskedasticity dynamic conditional correlation framework, which accounts for long memory, power effects, leverage terms, and time-varying correlations. The empirical analysis shows a contagion effect for Brazil and Mexico during the early stages of the global financial crisis, indicating signs of “recoupling.” Nevertheless, linkages show a general pattern of “decoupling” after the Lehman Brothers collapse. Furthermore, correlations between Brazil and the US are decreased from early 2009 onwards, implying that their dependence is larger in bearish than in bullish markets.
... For thorough surveys of the available Multivariate GARCH models and their use in various fields of risk management such as option pricing, hedging and portfolio selection see Bauwens, Laurent, and Rombouts (2006) and Silvennoinen and Teräsvirta (2009). Conrad, Karanasos, and Zeng (2011) applied a multivariate fractionally integrated asymmetric power ARCH (FIAPARCH) model that combines long memory, power transformations of the conditional variances , and leverage effects with constant conditional correlations (CCC) on eight national stock market indices returns. The long-range volatility dependence, the power transformation of returns and the asymmetric response of volatility to positive and negative shocks are three features that improve the modelling of the volatility process of asset returns and its implications for the various risk management practices. ...
... There are some recent studies that use the DCC models of either Engle (2002) or Tse and Tsui (2002) with the FIAPARCH specification in the variance equation. Aloui (2011) uses daily stock index returns from Latin American markets for the period 1995–2009 and runs the multivariate FIAPARCH with Engle's DCC, assuming t-distributed innovations following Conrad et al. (2011). The DCCs generated are modelled separately with an AR(p)-GARCH(1,1) with intercept dummies for the crisis events in the mean and the variance equation. ...
... These three features augment the traditional GARCH model in a suitable way to adequately fit the volatility process . The Wald tests applied support the particular augmented model and are in line with the results of Conrad et al. (2011). The corresponding parameters are found robust to the structural breaks in the returns' and volatilities' series, since their estimated values in the subsamples are similar to those of the whole sample. ...
This paper applies the vector AR-DCC-FIAPARCH model to eight national stock market indices' daily returns from 1988 to 2010, taking into account the structural breaks of each time series linked to the Asian and the recent Global financial crisis. We find significant cross effects, as well as long range volatility dependence, asymmetric volatility response to positive and negative shocks, and the power of returns that best fits the volatility pattern. One of the main findings of the model analysis is the higher dynamic correlations of the stock markets after a crisis event, which means increased contagion effects between the markets. The fact that during the crisis the conditional correlations remain on a high level indicates a continuous herding behaviour during these periods of increased market volatility. Finally, during the recent Global financial crisis the correlations remain on a much higher level than during the Asian financial crisis.
... 3 Although many studies use various multivariate GARCH models in order to estimate DCCs among financial markets during the crisises (e.g. Celik, 2012; Wang and Moore, 2012; Creti et al., 2013; Hwang et al., 2013; Maghyereh et al., 2015), the forecasting superiority of FIAPARCH on other GARCH models is supported by Conrad et al. (2011) and Chkili et al. (2014). The FIAPARCH specifications are suitable for capturing stylized facts like long memory, asymmetry and leverage effects. ...
... is the gamma function. 7 Conrad et al. (2011) note that a sufficient condition for the conditional variance of the FIAPARCH model to be positive almost surely for all t is that ...
This article investigates the asymmetric and long memory volatility properties and dynamic conditional correlations (DCCs) between Brazilian, Russian, Indian, Chinese, and South African (BRICS) stock markets and commodity (gold and oil) futures markets, using the trivariate DCC-fractionally integrated asymmetric power autoregressive conditional heteroskedasticity (FIAPARCH) model. We identify significant asymmetric and long memory volatility properties and DCCs for pairs of BRICS stock and commodity markets, and variability in DCCs and Markov Switching regimes during economic and financial crises. Finally, we analyze optimal portfolio weights and time-varying hedge ratios, demonstrating the importance of overweighting optimal portfolios between BRICS stock and commodity assets.
... Another model used in the present study is the FIAPARCH model, which was developed by Tse (1998) and allows for long memory features without neglecting the asymmetry eff ects in conditional variance. The FIAPARCH model improves the fl exibility of conditional variance specifi cation by allowing asymmetric response of volatility to negative and positive shocks, data determining the power of the most powerful returns in estimable structure in the volatility model and long-term volatility dependence (Conrad et al., 2011). The FIAPARCH (p, d, q) model can be presented as follows (Tse, 1998): ...
... Second, DCC coefficients for the two markets are estimated. The conditional variance-covariance matrix of the residuals can be described as follows: 3 We leave the application of fractionally integrated specifications allowing for long memory in the variance equation (see Conrad et al., 2011) for future research. ...
The China's crude oil futures market (INE market), as it was first launched in late March of 2018, quickly draws much attention from global investors. In reference to the high frequency data, this research explores how well this new product reacts efficiently to international influences and to what extent it can be integrated with traditional benchmarks, such as WTI and Brent. The multivariate GARCH models are employed to capture the cross-market time-varying correlations, return and volatility spillovers, which are modified by incorporating the detected structural breaks in the return dynamics to improve the accuracy of model estimates. Empirical results indicate a strong integration of INE market with these international benchmarks. A high but time-varying correlation is observed with recurring highs around 0.7. Spillover effects have included significant bidirectional return and volatility spillovers between the INE and the international benchmark markets. Secondly, INE market appears to interact better with the Brent market than with the WTI market. Thirdly, structural breaks can influence correlations, the portfolio weights and hedge ratios. Lastly, the correlation between crude oil futures markets decreases significantly during the periods when structural breaks caused by economic and/or geopolitical events are identified. These findings have important implications in policy makings and economic decisions on portfolio management and hedging strategies.
... The FIGARCH representation includes the GARCH (when d = 0) and the IGARCH (Engle and Bollerslev, [12]) when d = 1 with the implications in terms of impact of a shock on the forecasts of future conditional variances. Considering all the features involved in this specification, Conrad et al. ([7]) point out some advantages of the FIAPARCH(p, d, q) class of models, namely ...
In this work, an optimal alarm system is developed to predict whether a financial time series modeled via Fractionally Integrated Asymmetric Power ARCH (FIAPARCH) models, up/downcrosses some particular level and give an alarm whenever this crossing is predicted. The paper presents classical and Bayesian methodology for producing optimal alarm systems. Both methodologies are illustrated and their performance compared through a simulation study. The work finishes with an empirical application to a set of data concerning daily returns of the Sao Paulo Stock Market.
... This model is able to increase the flexibility of conditional volatility specifications via allowing for long memory volatility, asymmetric response of volatility to both the positive and/or negative shocks as well as the power of returns. For FIaPaRCh model, the predictable structure in the volatility pattern is the strongest (Conrad et al., 2008). Besides that, FIaPaRCh model is also considered the stable model under special cases, whereby it able to nest the formulation without power effects. ...
This paper is undertaken to study the stylized facts of three international Shariah stock markets (i.e., FTSE China Shariah, FTSE Bursa Malaysia Emas Shariah and S & P Pan Asia Shariah) and its responses to the oil price shocks. Results denote the presence of volatility clustering and long memory volatility in the three international Shariah stock markets examined. Besides that, FTSE China Shariah and S & P Pan Asia Shariah stock markets illustrate the existence of leverage effect whereby bad news influences the volatility greatly as compared to good news. In contrast, there is no leverage effect captured in the FTSE Bursa Malaysia Emas Shariah stock market. Meanwhile, the effect of shocks to the conditional volatility displays a hyperbolic rather than an exponential decaying rate. In terms of impact of oil price shocks to the three international Shariah stock markets examined, Brent and WTI crude oil returns demonstrate significant responsive to the three international Shariah stock returns investigated. However, return volatility of Brent and WTI crude oil show insignificant responsive to three international Shariah stock returns and its volatility. Last but not least, the risk-return tradeoff parameter in overall is statistically insignificant for the three international Shariah stock markets examined.
... The FIAPARCH model increases the flexibility of the conditional variance specification by allowing (i) an asymmetric response of volatility to positive and negative shocks (by being able to trace the leverage effect), (ii) the data to determine the power of returns for which the predictable structure in the volatility pattern is the strongest , and (iii) long memory in volatility dependence, depending on the fractionally integrated process or differencing parameter d (Baillie et al., 1996). These features in the volatility processes of asset returns have major implications for asset allocations, optimal portfolio designs, benefits of portfolio diversification etc. (see, Conrad et al., 2011). It is also worth noting that the FIAPARCH model nests two major classes of ARCH-type models: the APARCH and the FIGARCH models. ...
... Particularly, in a more stable monetary environment, common stock is a more effective hedge 7 See Cukierman and Meltzer (1986), Ungar and Zilberfarb (1993), Holland (1995). 8 See for example Braun et al. (1995), Lee (1998), Elder (2004, Wei (2008), Karonasos et al. (2006), Conrad et al. (2010Conrad et al. ( .2011, Karanasos and Zeng (2013), Zeng (2013), and many others. ...
This paper employs a constant conditional correlation bivariate EGARCH-in-mean model to investigate interactions among the rate of inflation, stock returns and their respective volatilities. This approach is capable of accommodating all the possible causalities among the four variables simultaneously, and therefore could deliver contemporary evidence of the nexus between monetary stability and stock market. The postwar dataset of the US inflation and stock returns is divided into pre- and post- Volcker period and the estimation results show some significant changes of inflation-stock return relation, as well as indirect links between two volatilities. The core findings in this study suggest that promoting monetary stability contributes to more mutual interactions among the four variables, in particular, common stock is a more effective hedge against inflation, and the level of inflation rate is central to explaining the relation between the two volatilities.
... where ω ∈ (0, ∞), |β| and |φ| < 1, 0 ≤ d ≤ 1, γ is the leverage coefficient and δ is the parameter for the power term that takes finite positive values, while (1 − L) d is the financial differencing operator expressed in terms of a hypergeometric function (see Conrad et al. (2008) for the expression of this function). ...
This paper focuses on developments in the European Economic and Monetary Union sovereign debt markets in the past decade. The first part analyzes the integration and segmentation structure of the bond markets of the Economic and Monetary Union before and after the sovereign debt crisis, by introducing the novel concept of correlation-based stable networks. Accordingly, a fair integration is observed between the bond markets during the pre-crisis period. However, a strict segmentation emerges, separating the members struggling with debt problems and the ones with relatively strong fiscal performances during the sovereign debt turmoil. The segmentation structure is clearly visualized, revealing the potential paths for crisis and recovery transmission in the future. In the second part, the paper comments on the recent decreasing trend in Economic and Monetary Union member bond yields and their increasing degree of co-movement. Accordingly, the paper argues that these changes do not depend on the fiscal performances of the member countries, but depend on the illusion of quality that appeared with the Fed (U.S. Federal Reserve) tapering signals in early 2013.
... All these factors have considerably raised the degree of stock market integration and promoted empirical research focused on international stock market co-movement. On the empirical side, this main research issue has been basically apprehended in the international finance literature and various empirical methodologies including cointegration approach (Arouri et al., 2011), error correction models, univariate and multivariate ARCH/GARCH-type models (Lin et al., 1994;Theodossiou and Lee, 1993;Chiang et al., 2007;Ho and Tsui, 2003;Conrad et al., 2010;Aloui et al., 2011;Sedik and Williams, 2011) rolling bi-correlation tests (Lim et al., 2008), and copula theory (Ye et al., 2012;Rodriguez, 2007;Aloui et al., 2011;Samarakoon, 2011), were implemented to shed light on stock market co-movement and risk assessment. Overall, they concluded that stock market co-movement is not constant over time. ...
This paper examines the short term and long term dependencies between stock market returns for the Gulf Cooperation Council (GCC) Countries (Bahrain, Kuwait, Oman, Qatar, Saudi Arabia, and the United Arab Emirates) during the period 2005-2010. Our empirical investigation is based on the wavelet squared coherence which allows us to assess the co-movement in both time-frequency spaces. Our results reveal frequent changes in the pattern of the co-movements especially after 2007 for all the selected GCC markets at relatively higher frequencies. We further note an increasing strength of dependence among the GCC stock markets during the last financial crisis signifying enhanced portfolio benefits for investors in the short term relative to the long term. On the financial side, we uncover that the strength of co-movement between GCC markets may impact the multi-country portfolio's value at risk (VaR) levels. These findings provide potential implications for portfolio managers operating in the GCC region who are invited to consider co-movement through both frequencies and time when designing their portfolios.
... Further, the power terms (ı) are statistically significant, ranging from 1.6885 to 2.3494. When the series are very likely to follow a non-normal error distribution, then the superiority of a squared term (ı = 2) is lost and other power transformations may be more appropriate (Conrad et al., 2011). Thus, these estimates support the selection of the APARCH specification for modeling conditional variance of returns. ...
This paper examines the effects of quantitative easing (QE) announcements by the European Central Bank, the Bank of Japan and the Bank of England on exchange rate dynamics. Using intraday data of three major exchange rates (EUR/USD, GBP/USD, JPY/USD), we apply a univariate APARCH(1,1) model and include QE dummies to empirically investigate how exchange rates are affected in mean and volatility. The empirical results indicate: (i) a direct negative impact on GBP and JPY and no effect of their volatility around the QE announcements of the corresponding central banks, (ii) a delayed devaluation of EUR and an increase of its volatility before and after the ECB's announcements. Furthermore, the behaviour of dynamic conditional correlation among currencies is investigated across the QE announcements. We find a decline in the conditional correlation between EUR and GBP around the announcements by the BoE. These findings highlight the differences on the credibility and effectiveness of the monetary easing strategies and provide important implications from the investors’ and policy makers’ perspective.
... where Q is the unconditional covariance matrix of e t , and α D and β D are non-negative scalars fulfilling α D + β D b 1. Following Conrad and Karanasos (2010) and Rittler (2012), we impose the UEDCC-AGARCH (1, 1) structure on the conditional variances (multivariate fractionally integrated APARCH models could also be used, as in Conrad et al., 2011; Karanasos et al., forthcoming), and we also amend it by allowing the shock and volatility spillover parameters to be time varying: ...
We examine how the most prevalent stochastic properties of key financial time series have been affected during the recent financial crises. In particular we focus on changes associated with the remarkable economic events of the last two decades in the volatility dynamics, including the underlying volatility persistence and volatility spillover structure. Using daily data from several key stock market indices, the results of our bivariate GARCH models show the existence of time varying correlations as well as time varying shock and volatility spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang Seng, which became more prominent during the recent financial crisis. Our theoretical considerations on the time varying model which provides the platform upon which we integrate our multifaceted empirical approaches are also of independent interest. In particular, we provide the general solution for time varying asymmetric GARCH specifications, which is a long standing research topic. This enables us to characterize these models by deriving, first, their multistep ahead predictors, second, the first two time varying unconditional moments, and third, their covariance structure. (C) 2014 Published by Elsevier B.V.
... 6 The FIAPARCH model increases the flexibility of the conditional variance specification by allowing an asymmetric response of volatility to positive and negative shocks and longrange volatility dependence. Furthermore, it allows the data to determine the power of returns for which the predictable structure in the volatility pattern is the strongest, while provides superior forecasts relative to other GARCH family models (Conrad et al., 2011). 7Engle (2002)proposed a different form of the DCC model. ...
This paper investigates the contagion effects of the Global Financial Crisis (2007–2009) by examining ten sectors in six developed and emerging regions during different phases of the crisis. The analysis tests different channels of financial contagion across regions and real economy sectors by utilizing dynamic conditional correlation from the multivariate Fractionally Integrated Asymmetric Power ARCH (FIAPARCH) model. Evidence shows that the GFC can be characterized by contagion effects across regional stock markets and regional financial and non-financial sectors.
However, Developed Pacific region and some sectors in particular Consumer Goods, Healthcare and Technology across all regions seem to be less affected by the crisis, while the most vulnerable sectors are observed in the emerging Asian and European regions. Further, the analysis on a crisis phase level indicates that the most severe contagion effects exist after the failure of Lehman Brothers limiting the effectiveness of portfolio diversification.
... where ¯ Q is the unconditional covariance matrix of e t , and α D and β D are non-negative scalars fulfilling (2012), we impose the UEDCC-AGARCH(1, 1) structure on the conditional variances (multivariate fractionally integrated APARCH models could also be used, as in Conrad et al., 2011 or Karanasos et al., 2014), and we also amend it by allowing the shock and volatility spillovers parameters to be time varying: ...
We examine how the most prevalent stochastic properties of key financial time
series have been affected during the recent financial crises. In particular we
focus on changes associated with the remarkable economic events of the last two
decades in the mean and volatility dynamics, including the underlying
volatility persistence and volatility spillovers structure. Using daily data
from several key stock market indices we find that stock market returns exhibit
time varying persistence in their corresponding conditional variances.
Furthermore, the results of our bivariate GARCH models show the existence of
time varying correlations as well as time varying shock and volatility
spillovers between the returns of FTSE and DAX, and those of NIKKEI and Hang
Seng, which became more prominent during the recent financial crisis. Our
theoretical considerations on the time varying model which provides the
platform upon which we integrate our multifaceted empirical approaches are also
of independent interest. In particular, we provide the general solution for low
order time varying specifications, which is a long standing research topic.
This enables us to characterize these models by deriving, first, their
multistep ahead predictors, second, the first two time varying unconditional
moments, and third, their covariance structure.
We propose a theoretical framework for the heteroscedasticity, and in particular for the asymmetric volatility of asset returns. Our model is based on the assumption that some investors are subject to mental framing in a dynamic setting. The analysis of individual trading data confirms that, in line with our model, investors tilt their portfolio towards riskier (less risky) assets subsequent to losses (gains). Based on their behavior, we derive a volatility process that accounts for the asymmetry thoroughly investigated in previous empirical studies: the parameter estimation of our volatility model yields the predicted negative relationship between abnormal returns and ensuing volatility.
This study provides a holistic and quantitative overview of over 800 mathematical methods (e.g., financial and risk models, statistical tests, statistics and advanced algorithms) taken out of sampled scientific literature on quantitative modelling, particularly, from financial and risk modelling by applying a bibliometric approach from 2008 to 2019 and a citation network analysis. This is done to elaborate on the influence in the field after the Financial Crisis 2008. We present a content analysis of journals, main topics, applied data sets and frontiers within quantitative modelling and highlight details about quantitative features such as implemented models, algorithms and aggregated model-family combinations. Moreover, we describe explications and ties to empirical stylised facts (e.g., asymmetry or nonlinearity). Finally, we discuss insights such as our main finding, namely, the non-existence of a “single-best”-approach as well as the future prospects.
Return volatility usually presents a degree of persistence, which, although still consistent with an essential stationary process, cannot be adequately captured by standard autoregressive specifications. In this study, we examine the transmission mechanism across petroleum volatilities accounting for this stylized fact. To do so, we compute both time and frequency domain measures of connectedness based on variance decompositions from a fractionally integrated VAR (FIVAR). Our main findings summarize: (1) there is strong evidence of long-memory in petroleum volatilities, but no evidence of infinite variances; (2) an adequate quantification of spillovers must consider long-memory persistence explicitly; (3) spillovers are relatively high, but considerably lower than predicted in the traditional short-memory framework, especially at low frequencies. Thus, accounting for long-memory has asymmetric implications for different market participants.
This paper documents evidence of changes in the co-movement of stock returns and risk transmission among four South Asian stock markets over periods of regional market reform and global market instability. The sample period (1993–2015) is disaggregated into three sub-periods: before and after the establishment of the South Asian Federation of Exchanges (SAFE) and after the 2008 Global Financial Crisis. The principal components investigation and cointegration analysis conclude that the co-movement among stock returns in this region altered amidst a change in the institutional context and global economic uncertainty. Using a tetra-variate GARCH-BEKK model, we find that, after the establishment of SAFE, the interactions among the markets increased through volatility spillovers, but decreased through shock spillovers. In addition, there were more shock and volatility spillovers in the last sub-period as compared to the first two sub-periods, indicating that risk transmission across countries increased during the period of uncertainty. In particular, the Indian stock market was a risk spreader in South Asia after the setup of SAFE and its influence on the regional stock markets increased even further after the 2008 Global Financial Crisis.
We find ASEAN5 and G5 stock markets are weakly linked in normal conditions. ASEAN5 markets became more connected with G5 markets during global financial crisis, with stronger conditional correlations, a higher level of risk spillover-connectedness and intensive causal risk dependence. By implications, ASEAN5 stocks are both return enhancers and risk diversifiers in boom market conditions. The diversification benefits remain even during crisis times, albeit lesser. Over the longer term, the diversification benefits of a portfolio that includes both ASEAN5 and G5 stocks are recaptured as market linkages revert to some lower levels due to decreased crisis contagion.
The current paper studies equity markets for the contagion of squared index returns as a proxy for stock market volatility, which has not been studied earlier. The study examines squared stock index returns of equity in 35 markets, including the US, UK, Euro Zone and BRICS (Brazil, Russia, India, China and South Africa) countries, as a proxy for the measurement of volatility. Results from the conditional heteroskedasticity long memory model show the evidence of long memory in the squared stock returns of all 35 stock indices studied. Empirical findings show the evidence of contagion during the global financial crisis (GFC) and Euro Zone crisis (EZC). The intensity of contagion varies depending on its sources. This implies that the effects of shocks are not symmetric and may have led to some structural changes. The effect of contagion is also studied by decomposing the level series into explained and unexplained behaviors.
The analysis of time-varying correlation between stock prices and exchange rates in the context of international investments has been well researched in the literature in last few years. In this paper, we study the interdependence of exchange rates and stock prices for seven countries (Canada, Japan, Denmark, Hong Kong, Singapore, Mexico and Brazil). To do so, we both use the DCC-FIEGARCH and FIAPARCH-DCC models during the period spanning from January 1, 2000 until January 1, 2016. The empirical results suggest asymmetric responses in stock prices-exchange rates linkages, a high persistence of the conditional correlation. They also show bidirectional spillovers effects between different series. Moreover, the results indicate different behavior of exchange rates-stock prices nexus during the crisis periods, suggesting the need for specific policy measures. Finally, our findings offer investors, portfolios managers and policymakers insights on international portfolios and monetary.
The paper investigates whether Southern Mediterranean and Middle Eastern markets under the Euro–Mediterranean Partnership (Egypt, Lebanon, Morocco, Malta, and Turkey) have become more financially integrated with the European stock market over time. The findings suggest that the Turkish equity market is moderately integrated with the European market, while the other economies exhibit weak financial integration with Europe, supporting the idea that the partnership appears to have no effect on enhancing inter-market linkages for these economies. Therefore, these markets would be good destinations for international investors seeking attractive investment opportunities to diversify their equity portfolios. Structural changes in the cross-market integration do exist, which may be considered as a guide for international equity portfolio diversification over different subperiods. In addition, there is evidence of an increasing trend in conditional correlations for Egypt and Turkey, to varying degrees, over time, notably during the post global financial crisis of 2007–2008, thus revealing herding behavior during this period. Overall, investors should be wary of the variation of equity market integration over time before engaging in an investment at the level of portfolio management and diversification. Policymakers must be aware of the remoteness of the current achievements of the Euro–Mediterranean Partnership from the targets set in terms of financial development and economic growth.
Purpose
The purpose of this paper is to analyze the existence of volatility spillover effect in frontier markets. This study also examines whether any linkages exist among these markets or not.
Design/methodology/approach
Monthly data of regional frontier markets, from 2009 to 2016, are analyzed using Multivariate GARCH (BEKK and Dynamic Conditional Correlation (DCC)) models.
Findings
The result of cointegration test shows that the sample frontier markets are not linked in long run, and Granger causality test reveals that the markets under consideration do not cause each other even in the short run. BEKK test says that the effect of the arrival of shock from the own market does not last for longer, whereas shock from other markets lasts with the stronger persistence, and according to DCC test, the volatility spillover exists for all the markets.
Practical implications
The results of present study suggest that the frontier markets are not cointegrated in the long run as well as in the short run, which opens the doors for long-term investments in these markets in future, which may lead to decent returns. Long-term investors may draw the benefits from including the financial assets in their portfolios from these non-integrated frontier markets; nevertheless, they have to consider and implement diversification and hedging strategies during the period of financial turmoil, so as to protect themselves against economic and financial distress.
Originality/value
Significant work has been done on developed, developing and emerging markets but frontier markets are not explored much so far. This paper is an attempt to see the status of frontier stock markets as potential financial markets for diversification benefits.
This paper investigates the spread of the Global Financial Crisis (GFC) and the Eurozone Sovereign Debt Crisis (ESDC) to different market capitalization segments across countries and regions. Specifically, it tests for capitalization-specific contagion across both crises and their phases by examining large, medium and small capitalization indices of G-20 equity markets. The analysis across stable and the two crisis periods shows the existence of a stronger largecap transmission channel for the majority of countries. On the other hand, the contagion dynamics across the phases of the two crises do not provide a clear pattern of a specific cap size-based contagion across all markets. However, there is evidence that the Pacific region and the three cap groups of some individual markets of different regions are less severely affected. Further, all three cap groups of developed markets are mostly affected during the last phase of the ESDC, while emerging and frontier markets show a more diverse pattern of contagion across the phases of both crises. Finally, the Lehman Brothers’ collapse triggers a dramatic increase of the infection rate, while the ESDC seems to be more contagious than the GFC. JEL classifications: F30; G15 Keywords: Capitalization-specific contagion; global financial crisis; Eurozone debt crisis; dynamic conditional correlation; FIAPARCH
The purpose of this study is to investigate the link between bank credit standards (CS hereafter) and business cycle fluctuations. This is the first empirical study which attempts to examine whether business cycle affects bank CS. We use quarterly survey-data on CS taken from the Bank Lending Survey from 2003Q1 to 2016Q1, for 14 Euro-area countries. We find that business cycle and GDP growth trend exert a negative influence on CS, and thus business cycle and trend are two major drivers of the tightening or easing of the CS. We also find that the two components (cyclical and trend) of the real GDP decomposition affect in a symmetric way CS. Moreover, symmetry of impacts was found between the CS and the business cycle and trend for large vs. small firms. Our findings could be helpful for both the European bank regulatory authorities and for the banks’ loan officers when they are designing macroprudential policies. JEL classifications: E30, E32, E44, G21 Keywords: credit standards, business cycle, bank lending survey, loan supply
This paper analyzes Credit Default Swap spread dynamics to determine whether the sovereign Credit Default Swap market is subject to contagion effects. Analysis is performed on credit spreads data from 35 worldwide countries belonging to four different economic categories over a period from 2006 until 2014, covering the subprime crisis and the European sovereign debt crisis. A novel approach is proposed to estimate the Dynamic Conditional Correlations between CDS spreads using the AR(1)-FIEGARCH(1,d,1)-DCC model. Based on our findings, we put a slant on the financial market vulnerability, reinforced by contagion effects during the different phases of the crises. Furthermore, analysis of each country solely shows that contagion effects are sterner during the Eurozone crisis compared to the global financial crisis and that the level of exposure to crises differs across global markets and regions. Yet our approach provides evidences that crises spread to countries across the world regardless their economic status or geographical positions.
Purpose
The purpose of this paper is to examine the dynamic relationship between crude oil price volatility and stock markets in the emerging economies like BRIC (Brazil, Russia, India and China) countries in the context of sharp continuous fall in the crude oil price in recent times.
Design/methodology/approach
The stock price volatility is partly explained by volatility in crude oil price. The author adopt an Asymmetric Power ARCH (APARCH) model which takes into account long memory behavior, speed of market information, asymmetries and leverage effects.
Findings
For Bovespa, MICEX, BSE Sensex and crude oil there is an asymmetric response of volatilities to positive and negative shocks and negative correlation exists between returns and volatility indicating that negative information will create greater volatility. However, for Shanghai Composite positive information has greater effect on stock price volatility in comparison to negative information. The study results also suggest the presence long memory behavior and persistent volatility clustering phenomenon amongst crude oil price and stock markets of the BRIC countries.
Originality/value
The present study makes a number of contributions to the existing literature in the following ways. First, the author have considered crude oil prices up to January 31, 2016, so that the study can reflect the impact of declining trend of crude oil prices on the stock indices which is also regarded as “new oil price shock” to measure the volatility between crude oil price and stock market indices of BRIC countries. Second, the volatility is captured by APARCH model which takes into account long memory behavior, speed of market information, asymmetries and leverage effects.
This study examines the interdependence of US dollar exchange rates expressed in five emerging currencies. Focusing on different phases of the global financial and European sovereign debt crises, the aim of this paper is to examine how the dynamics of correlations between emerging exchange markets evolved from January 04, 2000 to July 11, 2014. To this end, we adopt a dynamic conditional correlation model into a multivariate Fractionally Integrated Asymmetric Power ARCH framework, which accounts for long memory, power effects, leverage terms and time varying correlations. The empirical findings indicate a general pattern of decrease in exchange rates correlations across the phases of the global financial crisis and the European sovereign debt crisis, suggesting the depreciation against US dollar and different vulnerability of the currencies. Moreover, our analysis supports the existence of a general pattern of increase in dynamic correlations across several phases of the two crises, indicating the existence of a “contagion effect”.
Purpose
The purpose of this paper is to study the scope for country diversification in international portfolios of mutual funds for the “core” EMU countries. The author uses a sample of daily returns for country indices of French, German and Italian funds to investigate the quest for international diversification. The author focuses on fixed-income mutual funds during the period of the financial market turmoil since 2007.
Design/methodology/approach
The author compute optimal portfolio allocations from both unconstrained and constrained mean-variance frameworks that take as input the out-of-sample forecasts for the conditional mean, volatility and correlation of country-level indices for funds returns. The author also applies a portfolio allocation model based on utility maximization with learning about the time-varying conditional moments. The author compares the out-of-sample forecasting performance of 12 multivariate volatility models.
Findings
The author finds that there is a “core” EMU country also for the mutual fund industry: optimal portfolios allocate the largest portfolio weight to German funds, with Italian funds assigned a lower weight in comparison to French funds. This result is remarkably robust across competing forecasting models and optimal allocation strategies. It is also consistent with the findings from a utility-maximization model that incorporates learning about time-varying conditional moments.
Originality/value
This is the first study on optimal country-level diversification for a mutual fund investor focused on European countries in the fixed-income space for the turmoil period. The author uses a large array of econometric models that captures the salient features of a period characterized by large changes in volatility and correlation, and compare the performance of different optimal asset allocation models.
Assume that for , (Z
t
) and are respectively uncorrelated and independent sequences of r.v’s having identical marginal distribution F(⋅ ), with zero mean and variance .
This paper analyzed the volatility behavior of Asian real estate investment trust (REIT) markets. The autoregressive conditional heteroscedasticity (ARCH)-family models were applied for the purpose of conducting the in-sample fitting test and out-of-sample forecasting test. Results showed that the fractional integrated EGARCH model was the best model in forecasting the volatility for most of the Asian REIT markets. The outcome of this study would be useful for REIT investors in understanding the volatility of the Asian REIT markets. Similarly, policy-makers can also make use of this information to create derivate pricing for the future.
To analyze the dynamic and asymmetric contagion reactions of financial markets during the last subprime crisis, this paper proposes a contagion reaction equation combined with the generalized auto regressive conditional heteroskedasticity process to develop a dynamic asymmetric contagion model, and then provides the Markov chain Monte Carlo estimation method of this new model. This paper then constructs an empirical study of two metals futures in China during the last subprime crisis period, applying the model to measure the impact of the contagion reactions as well as assess the model’s effectiveness. Our results show: (1) the financial contagion phenomenon is the reason why some financial markets experienced almost corresponding reactions during the subprime crisis; (2) financial contagion reactions behave conspicuously in three particular phases during the subprime crisis; (3) financial contagion reactions have predictive functions for financial market changes and can provide indicators for risk management during crisis periods.
In this paper we study the dynamic relationship between Islamic and conventional stock markets. We use six Dow Jones Islamic indices and their conventional counterparts. We adopt both univariate and multivariate GARCH type models for the period 2000–2014. The findings show that the DCC-FIAPARCH is the best to model conditional heteroskedsticity among three multivariate GARCH specifications.
This article examines the spillover effect between the U.S. market and five of the most important emerging stock markets namely those of the BRICS (Brazil, Russia, India, China and South Africa), and draws implications for portfolio risk modeling and forecasting. It gives consideration to periods before and after the recent global financial crisis (GFC). To this end, the bivariate DCC-FIAPARCH model, the modified ICSS algorithm and the Value-at-Risk (VaR) are employed to capture volatility spillovers, detect potential structural breaks and assess the portfolio market risks. Using the U.S. and the BRICS daily spot market indices for the period from September 1997 to October 2013, our empirical results show strong evidence of asymmetry and long memory in the conditional volatility and significant dynamic correlations between the U.S. and the BRICS stock markets. Moreover, we find several sudden changes in these markets with a common break date centered on September 15, 2008 which corresponds to the Lehman Brothers collapse. The Brazil, India, China and South Africa markets are strongly affected by the GFC, supporting the hypothesis of recoupling (with increased linkages). In contrast, the hypothesis of decoupling is supported for the Russian stock markets only. Finally, the skewed Student-t FIAPARCH models outperform and provide more accurate in-sample estimates and out-of-sample forecasts of VaR than the normal and Student-t FIAPARCH models in almost all cases. These results provide helpful information to financial risk managers, regulators and portfolio investors to determine the diversification benefits among these markets.
This study provides new evidence on emerging stock market contagion during the Global Financial crisis (GFC) and the Euro zone Sovereign Debt Crisis (ESDC). Focusing on the three emerging Baltic markets and developed European markets, proxied by the EUROSTOXX50 stock index, we explore asymmetric dynamic conditional correlation dynamics across stable and crisis periods. Empirical evidence indicates a diverse contagion pattern for the Baltic region across the two crises. Latvia and Lithuania were contagious during the GFC, while were insulated from the adverse effects of the ESDC. On the other hand, Estonia decoupled from the negative consequences during the global turmoil period, but recoupled during the ESDC. The results could be attributed to financial and macroeconomic characteristics of the Baltic countries before and after the turmoil periods and the introduction time of the Euro as a national currency.
The empirically most relevant stylized facts when it comes to modeling time-varying financial volatility are the asymmetric response to return shocks and the long memory property. Up till now, these have largely been modeled in isolation. To capture asymmetry also with respect to the memory structure, we introduce a new model and apply it to stock market index data. We find that although the effect on volatility of negative return shocks is higher than for positive ones, the latter are more persistent and relatively quickly dominate negative ones.
In this paper, we estimate the value-at-risk (VaR) for some Middle East and North African emerging stock markets (Egypt, Israel, Turkey and Morocco) for the short and the long trading positions. We check whether considering for LM, asymmetries and fat-tails in the stock return's behaviour offer more accurate VaR forecasts. We compute the VaR for two ARCH/GARCH-type models including FIGARCH and FIAPARCH under two density functions: student and skewed student. The obtained results point out that that accounting for long dependence in return and volatility, fat-tails and asymmetry provides better one-day-ahead VaR forecasts. Furthermore, the FIAPARCH model out-performs the other models in the VaR forecasts. Finally, the FIAPARCH model provides for all the stock market indexes the lowest number of violations under the Basel II rules, given a risk exposure at the 99% confidence level. Our results offer potential implications for MENA stock markets risk quantifications, policy regulations and hedging strategies.
The main aim of this article is to investigate the accuracy of the Multivariate Generalized Autoregressive Conditional Heteroskedasticity Model (M-GARCH) for the selection of the best investment portfolio. There is extended literature on M-GARCH in this field with a great number of studies using different sets of variables among them the returns of assets, the volatility of the assets in the investment portfolio, the maturity date of the asset etc. The origin of M-GARCH is associated with the elements of the Dynamic Conditional Correlations Model (DDCM) as proposed by Engle. An earlier version of DDCM with time variations in the correlation matrix has been developed by Bollerslev. DCCM offers flexibility by incorporating different levels of volatilities able to structure portfolios with a great number of assets. M-GARCH models take into account separate univariate GARCH models, associate with each asset in the portfolio, in order to form a complete M-GARCH model. The present article uses a multiple dimension classic M-GARCH volatility model on a data set consisting from three time series. The daily ASE index on stock returns (Athens), the DAX index (Germany) and the CAC index (France). For each national index, the continuously compounded return was estimated as rt=100[log(pt)-log(pt-1)], where pt is the price on day t.
In this paper, we investigate the volatility spillovers between sukuk and sharia-compliant stocks in GCC countries. A multivariate Fractionally Integrated Asymmetric Power ARCH model with dynamic conditional correlations (DCC) is estimated under Student-t distribution. We provide strong evidence of persistence behavior in sukuk and sharia stock volatilities and a time-varying negative correlation. Using the Bai and Perron (2003. Journal of Applied Econometrics, 18, 1) test, we uncover structural breakpoints in the DCCs path corresponding to extreme external events including the failure of Lehman Brother's on September 2008. Such extreme events have increased the magnitude of the dynamic correlations between sharia-stocks and sukuk. We estimate a modified DCC model with exogenous variables (DCCX), which allows for exogenous variables to impact the behavior of the DCC over time. We find significant behavioral shifts in the sukuk/sharia stock relationship, which can be explained by market liquidity, U.S. CDS spreads and crude oil prices. Our findings provide useful implications for Islamic fund managers operating in the GCC markets as well as for GCC policymakers.
This article uses the DCC-FIAPARCH model to examine the time-varying properties of conditional return and volatility of crude oil and US stock markets as well as their dynamic correlations over the period 1988–2013. Our results indicate that both the long memory and asymmetric behavior characterize the conditional volatility of oil and stock market returns. On the other hand, the dynamic conditional correlations (DCC) between the crude oil and US stock markets are affected by several economic and geopolitical events. When looking at the optimal design of an oil-stock portfolio, we find that investors in the US markets should have more stocks than crude oil asset in order to reduce their portfolio risk. Finally, the use of the DCC-FIAPARCH model that explicitly accounts for long memory and asymmetric volatility effects enables the investors to effectively hedge the risk of their stock portfolios with lower costs, compared to the standard DCC-GARCH model.
This paper addresses the question whether dual long memory (LM), asymmetry and structural breaks in stock market returns matter when forecasting the value at risk (VaR) and expected shortfall (ES) for short and long trading positions. We answer this question for the Gulf Cooperation Council (GCC) stock markets. Empirically, we test the occurrence of structural breaks in the GCC return data using the Inclan and Tiao (1994)’s algorithm and we check the relevance of LM using Shimotsu (2006) procedure before estimating the ARFIMA-FIGARCH and ARFIMA-FIAPARCH models with different innovations’ distributions and computing VaR and ES. Our results show that all the GCC market's volatilities exhibit significant structural breaks matching mainly with the 2008–2009 global financial crises and the Arab spring. Also, they are governed by LM process either in the mean or in the conditional variance which cannot be due to the occurrence of structural breaks. Furthermore, the forecasting ability analysis shows that the FIAPARCH model under skewed Student-t distribution turn out to improve substantially the VaR and the ES forecasts.
Using high frequency data, this paper examines the long memory property in the unconditional and conditional volatility of the USD/INR exchange rate at different time scales using the Local Whittle (LW), the Exact Local Whittle (ELW) and the FIAPARCH models. Results indicate that the long memory property remains quite stable across different time scales for both unconditional and conditional volatility measures. Results from the non-overlapping moving window approach indicate that the extreme events (such as the subprime crisis and the European debt crisis) resulted in highly persistent behavior of the USD/INR exchange rate and thus lead to market inefficiency. This paper also examines the long memory property in the realized volatility based on different time scale data. Results indicate that the realized volatility measures based on different scales of the high frequency data exhibit a consistent and stable long memory property. However, the realized volatility measures based on daily data exhibit lower degree of long-range dependence. This study has implications for traders and investors (with different trading horizons) and can be helpful in predicting expected future volatility and in designing and implementing trading strategies at different time scales.
We use univariate and multivariate GARCH-type models to investigate the properties of conditional volatilities of stock returns and exchange rates, as well as their empirical relationships. Taking three European stock markets and two popular US dollar exchange rates as case study, our results show strong evidence of asymmetry and long memory in the conditional variances of all the series considered. In multivariate settings we find that bilateral relationships between stock and foreign exchange markets are highly significant for France and Germany. Moreover, both the univariate FIAPARCH and bivariate CCC-FIAPARCH models provide more accurate in-sample estimates and out-of-sample forecasts than the other competing GARCH-based specifications in almost all cases. Finally, there is evidence to support the suitability of the FIAPARCH model in forecasting portfolio's market risk exposure and the existence of diversification benefits between stock and foreign exchange markets.
Consistency and asymptotic normality of quasi-maximum likelihood estimators (QMLEs) for the fractionally integrated asymmetric power ARCH (FIAPARCH) process are proved. The moment conditions are assumed only for standardized errors. We show the properties for a wide range of QMLEs including Gaussian QMLE.
This article contains a review of multivariate GARCH models. Most common GARCH models are presented and their properties considered. This also includes nonparametric and semiparametric models. Existing specification and misspecification tests are discussed. Finally, there is an empirical example in which several multivariate GARCH models are fitted to the same data set and the results compared.
Purpose
– The aim is to evaluate the performance of symmetric and asymmetric ARCH models in forecasting both the one‐day‐ahead Value‐at‐Risk (VaR) and the realized intra‐day volatility of two equity indices in the Athens Stock Exchange.
Design/methodology/approach
– Two volatility specifications are estimated, the symmetric generalized autoregressive conditional heteroscedasticity (GARCH) and the asymmetric APARCH processes. The data set consisted of daily closing prices of the General and the Bank indices from 25 April 1994 to 19 December 2003 and their intra day quotation data from 8 May 2002 to 19 December 2003.
Findings
– Under the VaR framework, the most appropriate method for the Bank index is the symmetric model with normally distributed innovations, while the asymmetric model with asymmetric conditional distribution applies for the General index. On the other hand, the asymmetric model tracks closer the one‐step‐ahead intra‐day realized volatility with conditional normally distributed innovations for the Bank index but with asymmetric and leptokurtic distributed innovations for the General index.
Originality/value
– As concerns the Greek stock market, there are adequate methods in predicting market risk but it does not seem to be a specific model that is the most accurate for all the forecasting tasks.
We propose a new time series representation of persistence in conditional variance called a long memory stochastic volatility (LMSV) model. The LMSV model is constructed by incorporating an ARFIMA process in a standard stochastic volatility scheme. Strongly consistent estimators of the parameters of the model are obtained by maximizing the spectral approximation to the Gaussian likelihood. The finite sample properties of the spectral likelihood estimator are analyzed by means of a Monte Carlo study. An empirical example with a long time series of stock prices demonstrates the superiority of the LMSV model over existing (short-memory) volatility models.
This paper develops a parametric family of models of generalized autoregressive heteroskedasticity (GARCH). The family nests the most popular symmetric and asymmetric GARCH models, thereby highlighting the relation between the models and their treatment of asymmetry. Furthermore, the structure permits nested tests of different types of asymmetry and functional forms. Daily U.S. stock return data reject all standard GARCH models in favor of a model in which, roughly speaking, the conditional standard deviation depends on the shifted absolute value of the shocks raised to the power three halves and past standard deviations.
The FI-A-PARCH process has been developed by Tse (1998) to model essential characteristics of financial market returns. However, due to the nonstationarity described by Níguez (2002) the process exhibits infinite conditional second moments and no statements about the autocovariance function can be derived. Thus, the new Hyperbolic A-PARCH model is considered, first introduced in Schoffer (2003). Subsequently the characteristics of this extension of the FI-A-PARCH process are inspected. It can be shown, that under certain parameter restrictions the intrinsic process as well as the process of conditional volatilities is stationary. Furthermore, for an asymmetric transformation of the conditional volatilities the presence of long memory is proven. Thus, the introduced model is able to reproduce the main characteristics of financial market returns such as volatility clustering, leptokurtosis, asymmetry and long memory. --
We propose a practical and flexible method to introduce skewness in multivariate symmetric distributions. Applying this procedure to the multivariate Student density leads to a multivariate skew-Student density, in which each marginal has a specific asymmetry coefficient. Combined with a multivariate GARCH model, this new family of distributions is found to be more useful than its symmetric counterpart for modelling stock returns and especially forecasting the Value-at-Risk of portfolios.
Recent empirical evidence demonstrates the presence of an important long-memory component in realized asset return volatility. We specify and estimate multivariate models for the joint dynamics of stock returns and volatility that allow for long memory in volatility without imposing this property on returns. Asset pricing theory imposes testable cross-equation restrictions on the system that are not rejected in our preferred specifications, which include a strong financial leverage effect. We show that the impact of volatility shocks on stock prices is small and short lived, in spite of a positive risk-return tradeoff and long memory in volatility. Copyright by the President and Fellows of Harvard College and the Massachusetts Institute of Technology.
The book is a collection of essays in honour of Clive Granger. The chapters are by some of the world'leading econometricians, all of whom have collaborated with or studied with (or both) Clive Granger. Central themes of Grangers work are reflected in the book with attention to tests for unit roots and cointegration, tests of misspecification, forecasting models and forecast evaluation, non-linear and non-parametric econometric techniques, and overall, a careful blend of practical empirical work and strong theory. The book shows the scope of Granger's research and the range of the profession that has been influenced by his work.
We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the coexistence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-in-mean effect is significant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type specifications according to standard criteria.
This paper investigates the issue of temporal ordering of the range-based volatility and turnover volume in the Korean market for the period 1995-2005. We examine the dynamics of the two variables and their respective uncertainties using a bivariate dual long-memory model. We distinguish volume trading before the Asia financial crisis from trading after the crisis. We find that the apparent long-memory in the variables is quite resistant to the presence of breaks. However, when we take into account structural breaks the order of integration of the conditional variance series decreases considerably. Moreover, the impact of foreign volume on volatility is negative in the pre-crisis period but turns to positive after the crisis. This result is consistent with the view that foreign purchases tend to lower volatility in emerging markets - especially in the first few years after market liberalization when foreigners are buying into local markets - whereas foreign sales increase volatility. Before the crisis there is no causal effect for domestic volume on volatility whereas in the post-crisis period total and domestic volumes affect volatility positively. The former result is in line with the theoretical underpinnings that predict that trading within domestic investor groups does not affect volatility. The latter result is consistent with the theoretical argument that the positive relation between the two variables is driven by the uninformed general public.
The possibility of specific long-memory temporal properties exponential marginal distributionals of absolute returns are considered for daily data for a number of markets and similar results are found in each case. Possible explanations are considered but no complete explanation is found. A fractionally integrated model is considered, found to require an unusual distribution for its inputs, has a poor forecasting performance, and its properties may be explained by a regime-switching process.
This paper examines the forecasting performance of four GARCH(1,1) models (GARCH, EGARCH, GJR and APARCH) used with three distributions (Normal, Student-t and Skewed Student-t). We explore and compare different possible sources of forecasts improvements: asymmetry in the conditional variance, fat-tailed distributions and skewed distributions. Two major European stock indices (FTSE 100 and DAX 30) are studied using daily data over a 15-years period. Our results suggest that improvements of the overall estimation are achieved when asymmetric GARCH are used and when fat-tailed densities are taken into account in the conditional variance. Moreover, it is found that GJR and APARCH give better forecasts than symmetric GARCH. Finally increased performance of the forecasts is not clearly observed when using non-normal distributions.
The long memory characteristic of financial market volatility is well documented and has important implications for volatility forecasting and option pricing. When fitted to the same data, different volatility models calculate the unconditional variance differently and could have very different volatility persistent parameters. Hence, they produce very different volatility forecasts even when the projection is just beyond a few days. The popular GARCH and GJR models have short memory. This paper compares the out-of-sample forecasting performance of four long memory volatility models, viz. fractional integrated (FI), break, component and regime switching. Using S&P 500 returns, we find structural break model to produce the best in-sample fit and out-of-sample forecasts, if future volatility breaks are known. Without knowing the future breaks, GJR produced the best short horizon forecasts. For volatility forecasts of 10 days and beyond, FI dominates. The FI model projects the future unconditional variance from the exponentially weighted sum of an infinite number of past shocks. The persistence parameters then control how fast the forecasts converge to this unconditional variance. As the fractional differencing parameter gets closer to and exceeds 0.5, volatility is non-stationary. The success of the FI model in forecasting S&P 500 volatility suggests that the latter should be treated as nonstationary. Which volatility model is best for forecasting is an empirical issue. A best model for S&P 500 need not be the best for the other series, and may not always be the best, all the time, for forecasting S&P 500 volatility. Unusual events such as the 1987 crash, for example, call for unusual treatments to get better forecasting performance.
In this paper we model Value-at-Risk (VaR) for daily asset returns using a collection of parametric univariate and multivariate models of the ARCH class based on the skewed Student distribution. We show that models that rely on a symmetric density distribution for the error term underperform with respect to skewed density models when the left and right tails of the distribution of returns must be modelled. Thus, VaR for traders having both long and short positions is not adequately modelled using usual normal or Student distributions. We suggest using an APARCH model based on the skewed Student distribution (combined with a time-varying correlation in the multivariate case) to fully take into account the fat left and right tails of the returns distribution. This allows for an adequate modelling of large returns defined on long and short trading positions. The performances of the univariate models are assessed on daily data for three international stock indexes and three US stocks of the Dow Jones index. In a second application, we consider a portfolio of three US stocks and model its long and short VaR using a multivariate skewed Student density. Copyright © 2003 John Wiley & Sons, Ltd.
We investigate the impact of the European Central Bank's monetary policy communication during the press conference held after the monthly Governing Council meeting on the EUR-USD exchange rate in high frequency. Based on the method of Content Analysis, we construct communication indicators for the introductory statement and find that communication with respect to future price developments is most relevant. In response to statements about increasing risks to price stability the EUR appreciates on impact. To the contrary, communication about economic activity and monetary aggregates does not generate significant exchange rate reactions. Copyright (c) 2010 The Ohio State University.
This book provides an introduction to the methods employed in forecasting the future state of the economy. It provides a comprehensive coverage of methods and applications in this fast-growing area and is intended for use in postgraduate and upper-level undergraduate courses. Part I outlines the available techniques, particularly those used in business forecasting and econometric forecasting. The state of the art in time series modelling is reviewed and includes a discussion of Box-Jenkins models, the vector autogressive approach and cointegration. Ways of combining forecasts are also examined in detail. Part II considers the most important applications of forecasting. Applications in microeconomics include demand and sales forecasting, the use of anticipations data, leading indicators and scenario analysis. In macroeconomics the emphasis is on why errors occur in forecasting asset market prices, including implications of the efficient markets hypothesis for foreign markets, stock market prices and commodity market prices. The book ends with a discussion of the appropriateness of various techniques, recent developments in forecasting, and the links between economic forecasting and government policy.
Abstract: This work extends the analysis of Baillie, Bollerslev and Mikkelsen (1996) and Bollerslev and Mikkelsen (1996) on the estimation and identification problems of the Fractionally Integrated Generalized Autoregressive Conditional Heteroskedastik (FIGARCH) model. We assess the power of different information criteria and tests in identifying the presence of long memory in the conditional variances. The analysis is performed with a Montecarlo simulation study. In detail, the focus on the Akaike, Hannan-Quinn, Shibata and Schwarz information criteria and on the Jarque-Bera test for normality, Box-Pierce test for residual correlation and Engle test for ARCH effects. This study verifies that information criteria clearly distinguish the presence of long memory while tests do not evidence any difference between the fitted long and short memory models. An empirical application is provided; it analyses, on a high frequency dataset, the returns of the FIB30, the future on the MIB30, the Italian stock market index of highly capitalized firms.
The existing literature contains conflicting evidence regarding the relative quality of stock market volatility forecasts. Evidence can be found supporting the superiority of relatively complex models (including ARCH class models), while there is also evidence supporting the superiority of more simple alternatives. These inconsistencies are of particular concern because of the use of, and reliance on, volatility forecasts in key economic decision-making and analysis, and in asset/option pricing. This paper employs daily Australian data to examine this issue. The results suggest that the ARCH class of models and a simple regression model provide superior forecasts of volatility. However, the various model rankings are shown to be sensitive to the error statistic used to assess the accuracy of the forecasts. Nevertheless, a clear message is that volatility forecasting is a notoriously difficult task.
The new class of Fractionally Integrated Generalized AutoRegressive Conditionally Heteroskedastic (FIGARCH) processes is introduced. The conditional variance of the process implies a slow hyperbolic rate of decay for the influence of lagged squared innovations. Unlike (I(d) processes for the mean, Maximum Likelihood Estimates (MLE) of the FIGARCH parameters are argued to be . The small-sample behavior of an approximate MLE procedure is assessed through a simulation study, which also documents how the estimation of a standard GARCH model tends to produce integrated, or IGARCH, like estimates. An empirical example with daily Deutschmark — U.S. dollar exchange rates illustrates the practical relevance of the new FIGARCH specification.
We show that the empirical ranking of volatility models can be inconsistent for the true ranking if the evaluation is based on a proxy for the population measure of volatility. For example, the substitution of a squared return for the conditional variance in the evaluation of ARCH-type models can result in an inferior model being chosen as ‘best’ with a probability that converges to one as the sample size increases. We document the practical relevance of this problem in an empirical application and by simulation experiments. Our results provide an additional argument for using the realized variance in out-of-sample evaluations rather than the squared return. We derive the theoretical results in a general framework that is not specific to the comparison of volatility models. Similar problems can arise in comparisons of forecasting models whenever the predicted variable is a latent variable.
In this article we derive convenient representations for the cumulative impulse response function of the long memory GARCH(p, d, q) (LMGARCH) process. Our results extend the results in Baillie et al. (1996) [Baillie, R.T., Bollerslev, T., Mikkelsen, H.O. 1996. Fractionally integrated generalized autoregressive conditional heteroskedasticity. Journal of Econometrics 74, 3–30.] on the first order LMGARCH. Using the derived impulse response functions we compare the persistence of shocks to the conditional variance in various GARCH models of interest such as stable, integrated and LMGARCH.
We extend the fractionally integrated exponential GARCH (FIEGARCH) model for daily stock return data with long memory in return volatility of Bollerslev and Mikkelsen (1996) by introducing a possible volatility-in-mean effect. To avoid that the long memory property of volatility carries over to returns, we consider a filtered FIEGARCH-in-mean (FIEGARCH-M) effect in the return equation. The filtering of the volatility-in-mean component thus allows the co-existence of long memory in volatility and short memory in returns. We present an application to the daily CRSP value-weighted cum-dividend stock index return series from 1926 through 2006 which documents the empirical relevance of our model. The volatility-in-mean effect is significant, and the FIEGARCH-M model outperforms the original FIEGARCH model and alternative GARCH-type specifications according to standard criteria.
This paper introduces a new long memory volatility process, denoted by adaptive FIGARCH, or A-FIGARCH , which is designed to account for both long memory and structural change in the conditional variance process. Structural change is modeled by allowing the intercept to follow the smooth flexible functional form due to Gallant (1984. The Fourier flexible form. American Journal of Agricultural Economics 66, 204–208). A Monte Carlo study finds that the A-FIGARCH model outperforms the standard FIGARCH model when structural change is present, and performs at least as well in the absence of structural instability. An empirical application to stock market volatility is also included to illustrate the usefulness of the technique.
This paper uses Garch models to estimate the objective and risk-neutral density functions of financial asset prices and by comparing their shapes, recover detailed information on economic agents' attitudes toward risk. It differs from recent papers investigating analogous issues because it uses Nelson's result that Garch schemes are approximations of the kind of differential equations typically employed in finance to describe the evolution of asset prices. This feature of Garch schemes usually has been overshadowed by their well-known role as simple econometric tools providing reliable estimates of unobserved conditional variances. We show instead that the diffusion approximation property of Garch gives good results and can be extended to situations with (i) non-standard distributions for the innovations of a conditional mean equation of asset price changes and (ii) volatility concepts different from the variance. The objective PDF of the asset price is recovered from the estimation of a nonlinear Garch fitted to the historical path of the asset price. The risk-neutral PDF is extracted from cross-sections of bond option prices, after introducing a volatility risk premium function. The direct comparison of the shapes of the two PDFs reveals the price attached by economic agents to the different states of nature. Applications are carried out with regard to the futures written on the Italian 10-year bond.
This paper investigates the issue of temporal ordering of the range-based volatility and turnover volume in the Korean market for the period 1995–2005. We examine the dynamics of the two variables and their respective uncertainties using a bivariate dual long-memory model. We distinguish volume trading before the Asia financial crisis from trading after the crisis. We find that the apparent long-memory in the variables is quite resistant to the presence of breaks. However, when we take into account structural breaks the order of integration of the conditional variance series decreases considerably. Moreover, the impact of foreign volume on volatility is negative in the pre-crisis period but turns to positive after the crisis. This result is consistent with the view that foreign purchases tend to lower volatility in emerging markets—especially in the first few years after market liberalization when foreigners are buying into local markets—whereas foreign sales increase volatility. Before the crisis there is no causal effect for domestic volume on volatility whereas in the post-crisis period total and domestic volumes affect volatility positively. The former result is in line with the theoretical underpinnings that predict that trading within domestic investor groups does not affect volatility. The latter result is consistent with the theoretical argument that the positive relation between the two variables is driven by the uninformed general public.
The use of a conditionally unbiased, but imperfect, volatility proxy can lead to undesirable outcomes in standard methods for comparing conditional variance forecasts. We motivate our study with analytical results on the distortions caused by some widely used loss functions, when used with standard volatility proxies such as squared returns, the intra-daily range or realised volatility. We then derive necessary and sufficient conditions on the functional form of the loss function for the ranking of competing volatility forecasts to be robust to the presence of noise in the volatility proxy, and derive some useful special cases of this class of “robust” loss functions. The methods are illustrated with an application to the volatility of returns on IBM over the period 1993 to 2003.
In this paper, we investigate the effects of official interventions on the (short run) evolution and volatility of exchange rates. To this aim, we rely on a new measure of volatility implied by the FIGARCH model that outperforms the traditionally used GARCH one. It is found that central bank interventions exert an incorrectly signed effect on the levels of exchange rates and tend to increase their volatility in the short run. In general, our results also show that the traditional GARCH estimations tend to underestimate the effects in terms of volatility.
Ding et al. (1993) [Ding, Z., Granger, C.W.J., Engle, R.F., 1993. A long memory property of stock market returns and a new model. Journal of Empirical Finance1, 83–106] suggested a model which extends the ARCH family of models for analyzing a wider class of power transformations than simply taking the absolute value or squaring the data as in the conventional conditional heteroscedastic models. This paper analyzes the applicability of these power ARCH (PARCH) models to national stock market returns for 10 countries plus a world index. We find the PARCH model to be generally applicable once GARCH and leverage effects are taken into consideration. In addition, we also find that the optimal power transformation is remarkably similar across countries.
This paper shows that occasional breaks generate slowly decaying autocorrelations and other properties of I(d) processes, where d can be a fraction. Some theory and simulation results show that it is not easy to distinguish between the long memory property from the occasional-break process and the one from the I(d) process. We compare two time series models, an occasional-break model and an I(d) model to analyze S&P 500 absolute stock returns. An occasional-break model performs marginally better than an I(d) model in terms of in-sample fitting. In general, we found that an occasional-break model provides less competitive forecasts, but not significantly. However, the empirical results suggest a possibility such that, at least, part of the long memory may be caused by the presence of neglected breaks in the series. We show that the forecasts by an occasional break model incorporate incremental information regrading future volatility beyond that found in I(d) model. The findings enable improvements of volatility prediction by combining I(d) model and occasional-break model.
Given two sources of forecasts of the same quantity, it is possible to compare prediction records. In particular, it can be useful to test the hypothesis of equal accuracy in forecast performance. We analyse the behaviour of two possible tests, and of modifications of these tests designed to circumvent shortcomings in the original formulations. As a result of this analysis, a recommendation for one particular testing approach is made for practical applications.
This paper explores the return volatility predictability inherent in high-frequency speculative returns. Our analysis focuses on a refinement of the more traditional volatility measures, the integrated volatility, which links the notion of volatility more directly to the return variance over the relevant horizon. In our empirical analysis of the foreign exchange market the integrated volatility is conveniently approximated by a cumulative sum of the squared intraday returns. Forecast horizons ranging from short intraday to 1-month intervals are investigated. We document that standard volatility models generally provide good forecasts of this economically relevant volatility measure. Moreover, the use of high-frequency returns significantly improves the longer run interdaily volatility forecasts, both in theory and practice. The results are thus directly relevant for general research methodology as well as industry applications.
This paper provides a survey and review of the major econometric work on long memory processes, fractional integration, and their applications in economics and finance. Some of the definitions of long memory are reviewed, together with previous work in other disciplines. Section 3 describes the population characteristics of various long memory processes in the mean, including ARFIMA. Section 4 is concerned with estimation and examines semiparametric procedures in both the frequency and time domain, and also the properties of various regression based and maximum likelihood techniques. Long memory volatility processes are discussed in Section 5, while Section 6 discusses applications in economics and finance. The paper also has a concluding section.
Broad classes of diagnostics for serial correlation and/or dynamic conditional heteroskedasticity of regression disturbances are considered. The classes include statistics with good power against strongly dependent alternatives, along with the usual ones that test against weak dependence, and many others. Limiting null distributions are obtained, under mild conditions on the dependence structure of the alternative against which the test is derived, on moments of the disturbances, and on the regressors. The various test statistics have a similar overall structure, and while tests against strongly dependent alternatives entail more computation than ones against weakly dependent alternatives, the difference can be slight if the fast Fourier transform is used.
We use a long series of monthly data that spans over 100 years to examine the dynamics of US ex-post and ex-ante real interest rates. The principal tenet of this study is that the data are not consistent with a unit root in real interest rates, although shocks impinging upon these rates are rather persistent. In addition, our results highlight the importance of modeling long memory not only in the conditional mean but in the power transformed conditional variance as well. Overall, these findings suggest that much more attention needs to be paid to the degree of persistence and its consequences for the economic theories which are still inconsistent with the finding of either near-unit-root or long memory mean-reverting behavior.
This paper extends the work by Ding, Granger, and Engle (1993) and further examines the long memory property for various speculative returns. The long memory property found for S&P 500 returns is also found to exist for four other different speculative returns. One significant difference is that for foreign exchange rate returns, this property is strongest when instead of at d = 1 for stock returns. The theoretical autocorrelation functions for various GARCH(1, 1) models are also derived and found to be exponential decreasing, which is rather different from the sample autocorrelation function for the real data. A general class of long memory models that has no memory in returns themselves but long memory in absolute returns and their power transformations is proposed. The issue of estimation and simulation for this class of model is discussed. The Monte Carlo simulation shows that the theoretical model can mimic the stylized empirical facts strikingly well.
In the paper we study the relationship between macroeconomic and stock market volatility, using S&P500 data for the period 1970–2001. We find evidence of a twofold linkage between stock market and macroeconomic volatility. Firstly, the break process in the volatility of stock returns is associated with the break process in the volatility of the Federal funds rate and M1 growth. Secondly, two common long memory factors, mainly associated with output and inflation volatility, drive the break-free volatility series. While stock market volatility also affects macroeconomic volatility, the causality direction is stronger from macroeconomic to stock market volatility.
In this article we derive conditions which ensure the non-negativity of the conditional variance in the Hyperbolic GARCH(p,d,q) (HYGARCH) model of Davidson (2004). The conditions are necessary and sufficient for p=1 and sufficient for p≥2 and emerge as natural extensions of the inequality constraints derived in Nelson and Cao (1992) and Tsai and Chan (2008) for the GARCH model and in Conrad and Haag (2006) for the FIGARCH model. As a by-product we obtain a representation of the ARCH(∞) coefficients which allows computationally efficient multi-step-ahead forecasting of the conditional variance of a HYGARCH process. We also relate the necessary and sufficient parameter set of the HYGARCH to the necessary and sufficient parameter sets of its GARCH and FIGARCH components. Finally, we analyze the effects of erroneously fitting a FIGARCH model to a data sample which was truly generated by a HYGARCH process. Empirical applications of the HYGARCH(1,d,1) model to daily NYSE and DAX30 data illustrate the importance of our results.
In this paper, we consider testing distributional assumptions in multivariate GARCH models based on empirical processes. Using the fact that joint distribution carries the same amount of information as the marginal together with conditional distributions, we first transform the multivariate data into univariate independent data based on the marginal and conditional cumulative distribution functions. We then apply the Khmaladze's martingale transformation (K-transformation) to the empirical process in the presence of estimated parameters. The K-transformation eliminates the effect of parameter estimation, allowing a distribution-free test statistic to be constructed. We show that the K-transformation takes a very simple form for testing multivariate normal and multivariate t-distributions. The procedure is applied to a multivariate financial time series data set.
We compare 330 ARCH-type models in terms of their ability to describe the conditional variance. The models are compared out-of-sample using DM- exchange rate data and IBM return data, where the latter is based on a new data set of realized variance. We find no evidence that a GARCH(1,1) is outperformed by more sophisticated models in our analysis of exchange rates, whereas the GARCH(1,1) is clearly inferior to models that can accommodate a leverage effect in our analysis of IBM returns. The models are compared with the test for superior predictive ability (SPA) and the reality check for data snooping (RC). Our empirical results show that the RC lacks power to an extent that makes it unable to distinguish "good" and "bad" models in our analysis.
This paper introduces a new long memory volatility process, denoted by Adaptive FIGARCH, or A-FIGARCH, which is designed to account for both long memory and structural change in the conditional variance process. Structural change is modeled by allowing the intercept to follow a slowly varying function, specified by Gallant (1984)'s flexible functional form. A Monte Carlo study finds that the A-FIGARCH model outperforms the standard FIGARCH model when structural change is present, and performs at least as well in the absence of structural instability. An empirical application to stock market volatility is also included to illustrate the usefulness of the technique.