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Dynamic structure of the spot price of crude oil: does time aggregation matter?
Abstract
This paper assesses nonlinear structures in the time series data generating mechanism of crude oil prices. We apply well-known univariate tests for nonlinearity, with distinct power functions over alternatives, but with different null hypotheses reflecting the existence of different concepts of linearity and nonlinearity in the time series literature. We utilize daily data on crude oil spot price for over 26 years, as well as monthly data on crude oil spot price for 41 years. Investigating the monthly price of crude oil along with the daily price distinguishes the approach of this paper from existing studies focusing on the time series structure of crude oil price. All the tests detect strong evidence of general nonlinear serial dependence, as well as nonlinearity in the mean, variance, and skewness functions in the daily spot price of crude oil. Since evidence of nonlinear dependence is less dramatic in monthly observations, nonlinear serial dependence is moderated by time aggregation in crude oil prices but not significantly.
... Long-term uncertainty in future oil prices can alter the incentives to develop new oil fields in oil-producing countries . In addition, structural change in the oil industry has introduced more complexity into both the oil industry and oil pricing policies and has led to considerable oil price volatility since 2014 (Aghababa and Barnett, 2016). Volatility in oil prices can also hinder the implementation of alternative energy policies in oil-consuming countries due to the effect of oil price volatility on the government and investors' decisionmaking. ...
... As this interaction between metallic commodities and energy commodities occurs, it is necessary to emphasize that oil market professionals -investors and regulators -need to be aware that the use of models assuming that energy markets are perfect markets becomes inconsistent with the data, as such an assumption excludes any nonlinear structure of stochastic solutions for the models. Furthermore, the existence of this non-linear structure implies the possibility of exploitable profit opportunities for speculators who can model and use such a time series structure (Aghababa and Barnett, 2016). ...
This paper explores the interconnections between metal and energy commodities by assessing the transmission of volatility within their futures markets. Achieved through the spillover index, the analysis reveals the impact of shocks on asset pairs—highlighting which assets absorb and transmit volatility, thereby explaining market connectivity. The dataset covers a period of twenty years of daily closing prices from the London Metals Exchange for a range of commodities. The Diebold and Yilmaz (2012) index, enriched by Baruník and Krehlík (2018) was used to reflect the changes in trends. The results obtained provide insights into market connectivity and the propagation of volatility during periods of economic distress. In this context, following the 2008 crisis, precious metals exhibited significant interconnectivity, with the emergence of Silver's vulnerability along with Gold's volatility tied to pre-crisis returns. Furthermore, copper's volatility reflects conditional correlations with market stock prices and other commodities particularly during economic downturns.
... Due to the large production of shale oil in Canada and US, the supply shock of crude oil becomes less often. This structural change introduces more complexity of oil pricing policy [2]. For example, US joined the oil producers' cartel, which makes the oil producing countries experience considerable difficultly in reaching a common agreement on oil supply that is directly affected the oil prices. ...
Focusing the period of Covid-19 since January of 2020, this research empirically study how inflation and the price of crude oil are related within the US data. The linear regression with ARCH(1) model is employed and our empirical results illustrate the significantly positive correlation between these two factors. We find that the CPI increase 9% with one unit increase in the crude oil price during Covid-19 period. Crude oil price, however, does not show such a significant effect on the other macroeconomic variable in the US during Covid-19 period, for example, real consumption and GDP.
... Previous studies have shown a strong relationship between oil price and the real economy (Serletis, 2012;Elder and Serletis, 2012;Azad & Serletis, 2023) and points to complexity and nonlinearity in oil price dynamics and its effects (Aghababa & Barnett, 2016). Oil price shocks have caused major economic recession in the US (Hamilton, 1983), regardless of the type of shock under consideration. ...
Our study revisits the relationship between oil prices and Islamic finance over the last two decades for developed and emerging countries through a multicriteria time series approach. Specifically, we assess this relationship during turbulent times, considering the effect of recent healthcare shock and oil price shock caused by the coronavirus disease (COVID-19) pandemic and war in Ukraine, respectively. Therefore, we built an Autoregressive Distributed Lag (ARDL) specification using multicriteria time series tests that dealt with variables that did not require any transformation (detrending, stationarity, etc.), allowing us to use maximum available information. Our results reveal two interesting findings. First, although the oil sector has a significant impact on Islamic stock indices, there is a lack of evidence regarding a cointegration relationship, suggesting the absence of a long-term relationship and therefore a mean reversion between these two markets, particularly in developed countries. Second, since COVID-19, a mean reversion in the Islamic stock market (for both developed and emerging countries) has occurred, suggesting the presence of a cointegration relationship and active adjustment mechanism. The channel of investor behavior and market anxiety appears to drive this error correction mechanism. These findings indicate oil price–Islamic finance integration and market inefficiency.
... Consequently, the influence of a supply shock has grown more restricted, primarily attributed to the shale oil production in Canada and the US, despite the design of OPEC and the collaboration involving the Kingdom of Saudi Arabia (KSA) and Russia to regulate the production of oil. Because of this transition in the petroleum industry, both the oil industry and oil pricing policies have become more complicated (Aghababa and Barnett, 2016), resulting in significant volatility in the oil prices since 2014. In recent times, Covid-19 has intensified the oil industry's complex nature since the ongoing outbreak has created a dual shock for the oil market (Bourghelle et al., 2021). ...
Volatility in natural resources commodity prices is prevailing for a longer period. However, after the Covid-19 pandemic, most economical and financial markets were affected, and the natural resources commodity market was greatly affected. Besides, the pandemic's closing or postponement of the industrial sector further fuels uncertainty in the natural resources commodity market. Therefore, it is important to analyze whether volatility exists in natural resources commodity prices during the pandemic period? In this regard, the current study investigated price volatility in copper and crude oil prices during the Covid-19 while using the most recent and extended dataset from January 02, 2019, to October 08, 2021, in the case of the US. For empirical examination, this study used the breakpoint unit root test, which illustrates that the leveled data is non-stationary while the first differenced data is stationary, where both leveled and first differenced data demonstrate the breakpoints in time series. This study uses the threshold generalized autoregressive conditional heteroscedasticity (TGARCH) and exponential generalized autoregressive conditional heteroscedasticity (EGARCH) to analyze natural resource commodity price volatility. The empirical findings uncover that both variables are volatile during the Covid-19 pandemic. However, the negative shock of the Covid-19 pandemic makes the crude oil price more volatile relative to copper prices. Besides, the previous variances are also positively associated with the current variances of both variables. The findings also reveal that copper could be a safe haven for reducing volatility in natural resources. Based on the empirical findings, this study suggests ensuring macroeconomic stability and reconsidering the traditional price-fixing or price ceiling policies to tackle volatility in the Covid-19 pandemic.
... The existence of non-linear behavior in the oil price series was already expected due to the existence of structural breaks. Some works in the literature also found a non-linear generating process for oil (see Kyrtsou, Malliaris and Serletis [58]; Aghababa and Barnett [59]; among others). ...
This paper proposes alternative methodologies for oil price forecasting using mixed-frequency data and a textual sentiment indicator. The latter variable was extracted from oil market reports issued by the Energy Information Administration. We used the root mean square error (RMSE) to evaluate the forecasting accuracy of the econometric models. Compared with other econometric models, the mixed data sampling (MIDAS) model with high-frequency financial indicators and the sentiment index as explanatory variables performs better for forecasting crude oil prices.
... A topic for future research would be to analyse the magnitude of the transmission of volatility between energy and metal commodities. In addition, as dependencies between oil and commodity prices are potentially nonlinear (Aghababa and Barnett, 2016) future research could incorporate nonlinearities in the models. ...
... The main argument behind this is the fact that around two-thirds of the global physical oil-trading uses the Brent as a reference price, primarily due to the "light"and "sweet"properties of Brent oil which render it ideal for transportation to distant locations. 1 In order to take ‡uctuations of exchange rates and in ‡ation into account, we follow Güntner (2014) and accordingly construct the national real oil price of each country. In doing so, we convert the Brent oil price from U.S dollars to national currency using the corresponding bilateral exchange rate as reported by the St. Louis Federal Reserve Economic Database (FRED), and then de ‡ate it using the domestic consumer price index (CPI), available from OECD. ...
This paper investigates mean and volatility spillovers between the crude oil market and three financial markets, namely the debt, stock, and foreign exchange markets, while providing international evidence from each of the seven major advanced economies (G7), and the small open oil-exporting economy of Norway. Using monthly data for the period from May 1987 to March 2016, and a four-variable VARMA-GARCH model with a BEKK variance specification, we find significant spillovers and interactions among the markets, but also absence of a hierarchy of influence from one specific market to the others. We further incorporate a structural break to examine the possible effects of the prolonged episode of zero lower bound in the aftermath of the
global financial crisis, and provide evidence of strengthened linkages from all the eight international economies.
Purpose
As specific objectives, we intend to: (1) measure the connectivity between the spillovers of returns from the financial and nonfinancial sectors of the Brazilian stock market; (2) estimate the spillovers of individual returns for each sector to identify periods of higher and lower profits over a period of around eight years; (3) investigate the existence of relationships between these repercussions between pairs of sectoral indices, evaluating how much each specific sector transfers to each other and the market as a whole and (4) examine whether the connectivity of the Brazilian stock market itself and future interest rates in the USA and Brazil as well as the risk of the Brazilian economy, were explanatory variables of the dynamics of interdependence in the returns of these indices.
Design/methodology/approach
With a daily series of closing prices of sectoral indices from March 3, 2015, until June 21, 2023, we researched eight of the most relevant sectoral indices on the São Paulo Stock Exchange (B3). With this data, we estimate the Diebold–Yilmaz spillover index and frequency decompositions of Barunik–Krehlik.
Findings
The conclusions indicate that there is an overall connection of 66% in the financial and nonfinancial sectoral indices, with a peak of 83%. The consumer, energy and public services sectors stand out as significant sources of primary spillovers. When we classified secondary effects into periods, we saw that the shocks dissipated as time passed and the returns of the commodity index remained resilient across all periods.
Originality/value
Our conclusions highlight the influence of three main factors in sectors with a high degree of connectivity: periods of increased uncertainty; negative externalities in post-crisis periods and the impact of financial news on market sentiment. We think this study provides information that can be useful for policymakers, investors, investment portfolio managers, economists (financial, monetary and industrial), investment consultants and researchers who are interested in the complex interconnection among emerging market stock indices.
We model the first and second moments of global crude oil benchmarks, using iterative pre-whitened generalized autoregressive conditional heteroskedasticity (GARCH) models and, in doing so, validate the efficacy of such models in assimilating the neglected nonlinearities in the underlying data-generating processes. The benchmarks considered for this study are Brent, Dubai/Oman, and West Texas Intermediate (WTI) crude oil. While nonlinear serial dependence happens to be a stylized fact across different asset classes, it is our view that prior scholarly contributions have not adequately untangled the effect of data aggregation (in time) in the examination of nonlinear dependencies. In this context, the present study strives to untangle the critical role that time aggregation plays in the examination of nonlinearity in global crude oil benchmarks using data at daily, weekly as well as monthly time frequencies. Our findings are as follows: the optimum GARCH models perform well in capturing all of the neglected nonlinearity in monthly returns of the crude benchmarks. When it comes to daily and weekly returns, our study reveals traces of neglected nonlinearities that are not completely captured by GARCH models. Moreover, such residual traces of neglected nonlinear dependencies are relatively more pronounced at the granular levels and become more and more elusory as the data get aggregated in time.
JEL codes: C22, C53, C58, G1, Q47
The recent coronavirus pandemic (COVID-19) has negatively impacted the whole economy, especially the oil industry, in at least two ways. First, it created a demand shock as COVID-19 reduced global demand for crude oil, increased uncertainty, and triggered a serious economic recession in most developed and emerging countries. Second, it led to a supply shock as the pandemic resulted in an oil trade war between the major oil-producing nations (Saudi Arabia and Russia). Both shocks led to very high levels of oil price volatility. Our paper explores the dynamics of this volatility and explains the effects of these two shocks (induced by an adjustment of oil demand and supply) on West Texas Intermediate (WTI) crude oil price volatility. Accordingly, we show that oil price volatility reacted substantially to the pandemic-induced oil shocks. In particular, we document the impact of uncertainty caused by these shocks and investor anxiety on oil price volatility. We show that greater uncertainty leads to more oil price volatility. Our findings remained unchanged even after controlling for modeling robustness.
In the present study, we investigate the long memory dynamics in crude oil markets from an adaptive market hypothesis (AMH) perspective. In doing so, we subject the three regional crude oil benchmarks, namely, West Texas Intermediate, Brent and Dubai crude prices to a rolling Hurst exponent analysis. Subsequently, we test for homogeneity in the degree of efficiency of crude oil benchmarks using a battery of nonparametric tests. In light of the heterogeneity in the degree of efficiency that was uncovered, we offer a relative ranking of the three benchmarks considered for the study. Our findings reveal WTI market to be relatively the most efficient followed by Brent and Dubai markets. Further, by using an extensive dataset of over 36 years, we find crude oil markets to be efficient for the most part of the study period, only to be interspersed with transient and short‐lived periods of market inefficiency. Lastly, the important implications that the study's findings have on various stakeholders are also discussed.
We classify all functions of multivariate stochastic processes having time-series estimates that are independent of data frequency. Such an estimator applied to high-frequency data may be used to infer properties of estimates relating to low-frequency data. Our property encompasses two previously-proposed time-aggregation properties (with limited solutions) as different special cases. Our general time-aggregating functions satisfy a pair of coupled second-order partial differential equations. We derive analytic solutions for arbitrary-dimensional martingales and log-martingales. The time-aggregation property of a time-series model is similar – indeed time-aggregating functions always correspond to point estimators based on expected values – but we do not propose a specific new forecasting model. However, we do derive time-aggregating unbiased and efficient estimators for nth-order moments of log returns, applying these results to problems facing portfolio managers who re-optimise portfolios or hedge their risks at lower frequencies than the frequency at which their risk premia are monitored.
This paper aims at modeling and forecasting volatility in both oil and USD exchange
rate markets using high frequency data. We test whether extreme co-movements
(co-jumps) between these markets, as well as intraday unexpected news,
help to improve volatility forecasting or not. Accordingly, we propose different
extensions of Corsi (2009)’s model by including co-jumps and news. Our analysis
provides two interesting findings. First, we find that both markets exhibit significant
co-jumps driven by unexpected macroeconomic news. Second, we show that
our model outperforms Corsi (2009)’s model and provides more accurate forecasts.
In particular, while co-jumps constitute a key variable in forecasting oil
price volatility, the unexpected news is relevant to forecasts of USD exchange rate
volatility.
Bu çalışmada Brent ham petrol
getirilerindeki kaotik dinamiklerin varlığı doğrusal olmama ve kaos testleri
yardımıyla araştırılmıştır. Bu amaçla 2009-2019 dönemleri arasında Brent ham
petrol günlük kapanış fiyat getirilerinden oluşan veri seti kullanılmıştır.
Öncelikle, BDS testi kullanılarak getirilerdeki doğrusal olmama test edilmiş ve
doğrusal olmayan yapının varlığına yönelik kanıt elde edilmiştir. Daha sonra,
getirilerin uzun hafızaya sahip olduğu GPH testi ile tespit edilmiştir. Son
olarak, korelasyon boyutu analizi kullanılarak günlük getirilerin başlangıç
durumlarına hassas bağlılık özelliği gösterdikleri görülmüştür. Tüm bulgular
bir arada değerlendirildiğinde Brent ham petrol günlük getirilerinin kaotik
dinamikler tarafından karakterize edildiği ve etkin piyasa hipotezinin geçerli
olmadığı tespit edilmiştir. Çalışmadaki tüm ampirik bulgular getiri serileri
için kısa dönemde öngörü yapılabileceğini, ancak uzun dönemli öngörü yapmanın
zor olduğu sonucuna işaret etmektedir.
This paper investigates mean and volatility spillovers between the crude oil market and three financial markets, namely the debt, stock, and foreign exchange markets, while providing international evidence from each of the seven major advanced economies (G7), and the small open oil-exporting economy of Norway. Using monthly data for the period from May 1987 to March 2016, and a four-variable VARMA-GARCH model with a BEKK variance specification, we find significant spillovers and interactions among the markets, but also absence of a hierarchy of influence from one specific market to the others. We further incorporate a structural break to examine the possible effects of the prolonged episode of zero lower bound in the aftermath of the global financial crisis, and provide evidence of strengthened linkages from all the eight international economies.
In this paper we study stock price adjustment dynamics in a nonlinear framework while examining their relationship with the oil market. Comparing four countries (USA, France, Mexico and the Philippines), we identify several significant findings. First, we highlight some evidence of considerable linkages between stock and oil markets and we show significant long-run relationships between these markets. Second, using nonlinear cointegration techniques, we propose an on/off nonlinear model to investigate time dependency and reproduce the linkages between the oil and stock markets. More interestingly, we identify different regimes for stock-oil price deviations and show a nonlinear mean-reverting mechanism which is activated by regime with an adjustment speed that increases according to price deviations toward the equilibrium.
This paper surveys the history of the oil industry with a particular focus on the events associated with significant changes in the price of oil. Although oil was used much differently and was substantially less important economically in the nineteenth century than it is today, there are interesting parallels between events in that era and more recent developments. Key post-World-War-II oil shocks reviewed include the Suez Crisis of 1956-57, the OPEC oil embargo of 1973-1974, the Iranian revolution of 1978-1979, the Iran-Iraq War initiated in 1980, the first Persian Gulf War in 1990-91, and the oil price spike of 2007-2008. Other more minor disturbances are also discussed, as are the economic downturns that followed each of the major postwar oil shocks.Institutional subscribers to the NBER working paper series, and residents of developing countries may download this paper without additional charge at www.nber.org.
This paper examines both the linear and nonlinear causal relationships between crude oil price changes and stock market returns for the United States. In particular, the study applied a battery of unit root tests to ascertain the time series properties of crude oil price changes and stock market returns. The linear and nonlinear causality tests were conducted through the standard VAR and the M-G frameworks, respectively. The results from both the linear and nonlinear unit root tests indicate that crude oil price changes and stock market returns are level stationary. The results from the standard VAR model provide evidence of bidirectional causality between crude oil price changes and stock market returns. The results from the M-G causality test support the finding of nonlinear bidirectional causality between crude oil price changes and stock market returns.
Although the assumption in the financial press is that fluctuations in the price of oil affect stock market prices, empirical evidence of the impact of these fluctuations on stock returns has been mixed. Unlike other empirical studies, which have focused largely on broad market indices (national and/or regional indices), our study adds to knowledge of the relationship between oil prices and stock markets in Europe by testing for short- and long-term links in the aggregate as well as sector by sector. We show that the response of stock returns to oil price changes differs greatly depending on the sector of activity. In particular, we show that changes in the price of oil have negative effects on short- and long-term stock prices in Food & Beverages.
All but one of the U.S. recessions since World War II have been preceded, typically with a lag of around three-fourths of a year, by a dramatic increase in the price of crude petroleum. This does not mean that oil shocks caused these recessions. Evidence is presented, however, that even over the period 1948-72 this correlation is statistically significant and nonspurlious, supporting the proposition that oil shocks were a contributing factor in at least some of the U.S. recessions prior to 1972. By extension, energy price increases may account for much of post-OPEC macroeconomic performance.
In this paper we test for deterministic chaos(i.e., nonlinear deterministic processes which look random) in seven Mont Belview, Texas hydrocarbon markets, using monthly data from 1985:1 to 1996:12 -- the markets are those of ethane, propane, normal butane, iso-butane, naphta, crude oil, and natural gas. In doing so, we use the Lyapunov exponent estimator of Nychka, Ellner, Gallant and McCaffrey (1992). We conclude that there is evidence consistent with chaotic nonlinear generation process in all five natural gas liquids markets.
[eng] Transportation costs and monopoly location in presence of regional disparities. . This article aims at analysing the impact of the level of transportation costs on the location choice of a monopolist. We consider two asymmetric regions. The heterogeneity of space lies in both regional incomes and population sizes: the first region is endowed with wide income spreads allocated among few consumers whereas the second one is highly populated however not as wealthy. Among the results, we show that a low transportation costs induces the firm to exploit size effects through locating in the most populated region. Moreover, a small transport cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. cost decrease may induce a net welfare loss, thus allowing for regional development policies which do not rely on inter-regional transportation infrastructures. [fre] Cet article d�veloppe une statique comparative de l'impact de diff�rents sc�narios d'investissement (projet d'infrastructure conduisant � une baisse mod�r�e ou � une forte baisse du co�t de transport inter-r�gional) sur le choix de localisation d'une entreprise en situation de monopole, au sein d'un espace int�gr� compos� de deux r�gions aux populations et revenus h�t�rog�nes. La premi�re r�gion, faiblement peupl�e, pr�sente de fortes disparit�s de revenus, tandis que la seconde, plus homog�ne en termes de revenu, repr�sente un march� potentiel plus �tendu. On montre que l'h�t�rog�n�it� des revenus constitue la force dominante du mod�le lorsque le sc�nario d'investissement privil�gi� par les politiques publiques conduit � des gains substantiels du point de vue du co�t de transport entre les deux r�gions. L'effet de richesse, lorsqu'il est associ� � une forte disparit� des revenus, n'incite pas l'entreprise � exploiter son pouvoir de march� au d�triment de la r�gion l
In this article, we examine whether WTI and Brent crude oil spot and futures prices (at 1, 3 and 6 months to maturity) contain a unit root with one and two structural breaks, employing weekly data over the period 1991-2004. To realise this objective we employ Lagrange multiplier (LM) unit root tests with one and two endogenous structural breaks proposed by Lee and Strazicich [2003. Minimum Lagrange multiplier unit root test with two structural breaks. Review of Economics and Statistics, 85, 1082-1089; 2004. Minimum LM unit root test with one structural break. Working Paper no. 04-17, Department of Economics, Appalachian State University]. We find that each of the oil price series can be characterised as a random walk process and that the endogenous structural breaks are significant and meaningful in terms of events that have impacted on world oil markets.
This paper proposes new tests for detecting the presence of a unit root in quite general time series models. Our approach
is nonparametric with respect to nuisance parameters and thereby allows for a very wide class of weakly dependent and possibly
heterogeneously distributed data. The tests accommodate models with a fitted drift and a time trend so that they may be used
to discriminate between unit root nonstationarity and stationarity about a deterministic trend. The limiting distributions
of the statistics are obtained under both the unit root null and a sequence of local alternatives. The latter noncentral distribution
theory yields local asymptotic power functions for the tests and facilitates comparisons with alternative procedures due to
Dickey & Fuller. Simulations are reported on the performance of the new tests in finite samples.
Two types of state-switching models for U.S. real output have been proposed: models that switch randomly between states and models that switch states deterministically, as in the threshold autoregressive model of Potter. These models have been justified primarily on how well they fit the sample data, yielding statistically significant estimates of the model coefficients. Here we propose a new approach to the evaluation of an estimated nonlinear time series model that provides a complement to existing methods based on in-sample fit or on out-of-sample forecasting. In this new approach, a battery of distinct nonlinearity tests is applied to the sample data, resulting in a set of p-values for rejecting the null hypothesis of a linear generating mechanism. This set of p-values is taken to be a "stylized fact" characterizing the nonlinear serial dependence in the generating mechanism of the time series. The effectiveness of an estimated nonlinear model for this time series is then evaluated in terms of the congruence between this stylized fact and a set of nonlinearity test results obtained from data simulated using the estimated model. In particular, we derive a portmanteau statistic based on this set of nonlinearity test p-values that allows us to test the proposition that a given model adequately captures the nonlinear serial dependence in the sample data. We apply the method to several estimated state-switching models of U.S. real output.
This paper considers two nonlinearity tests for stationary time series. The idea of Tukey's one degree of freedom for nonadditivity
test is generalized to the time series setting. The case of concurrent nonlinearity is discussed in detail. Simulation results
show that the proposed tests are more powerful than that of Keenan (1985).
In this chapter we use our battery of nonlinearity tests to study the time series properties of growth rates in common stock
prices at different levels of time aggregation. Financial economists call such growth rates “rates of return,” and express
them as decimal fractions. We also look at the effect of “hard clipping” the data in order to separate the issue of conditional
dependence in variance from the deeper issue of serial nonlinear dependence in the time series. By “hard clipping” we mean
a transformation that converts the data to a sequence of +1’s and −1’s, depending on whether the return is positive or negative.
Macroeconomic shocks such as wil price increases induce a systematic (endogenous) response of monetary policy. We develop a VAR-based technique for decomposing the total economic effects of a given exogenous shock into the portion attributable directly to the shock and the part arising from the policy response to the shock.
Squared-residual autocorrelations have been found useful in detecting non-linear types of statistical dependence in the residuals of fitted autoregressive-moving average (ARMA) models [cf. C. W. J. Granger and A. P. Andersen, An introduction to bilinear time series models. (1978; Zbl 0379.62074)]. In this note it is shown that the normalized squared-residual autocorrelations are asymptotically unit multivariate normal. The results of a simulation experiment confirming the small- sample validity of the proposed tests is reported.
Stable autoregressive (AR) and autoregressive moving average (ARMA) processes belong to the class of stationary linear time series. A linear time series {} is Gaussian if the distribution of the independent innovations {ε(t)} is normal. Assuming that Eε(t) = 0, some of the third-order cumulants cxxx=Ex(t)x(t+m)x(t+n) will be non-zero if the ε(t) are not normal and Eε3(t)≠O. If the relationship between {x(t)} and {ε(t)} is non-linear, then {x(t)} is non-Gaussian even if the ε(t) are normal. This paper presents a simple estimator of the bispectrum, the Fourier transform of {cxxx(m, n)}. This sample bispectrum is used to construct a statistic to test whether the bispectrum of {x(t)} is non-zero. A rejection of the null hypothesis implies a rejection of the hypothesis that {x(t)} is Gaussian. Another test statistic is presented for testing the hypothesis that {x(t)} is linear. The asymptotic properties of the sample bispectrum are incorporated in these test statistics. The tests are consistent as the sample size N→-∞
In this paper we investigate the asymmetric effects of oil price shocks and monetary policy on macroeconomic activity, using monthly data for the United States, over the period from 1983:1 to 2008:12. In doing so, we use a logistic smooth transition vector autoregression (VAR), as detailed in Terasvirta and Anderson (1992) and Weise (1999), and make a distinction between two oil price volatility regimes (high and low), using the realized oil price volatility as a switching variable. We isolate the effects of oil price and monetary policy shocks and their asymmetry on output growth and, following Koop et al. (1996) and Weise (1999), we employ simulation methods to calculate Generalized Impulse Response Functions (GIRFs) to trace the effects of independent shocks on the conditional means of the variables. Our results suggest that in addition to the price of oil, oil price volatility has an impact on macroeconomic activity and that monetary policy is not only reinforcing the effects of oil price shocks on output, it is also contributing to the asymmetric response of output to oil price shocks.
Purpose
While price studies such as Jawadi et al. generally focus on the relationships between oil and stock markets through the study of oil price on stock markets, this paper takes a different perspective to the linkages between oil and stock markets. This study sets out to investigate the efficiency hypothesis for oil markets while testing for whether oil price dynamics depend on stock market fluctuations or not.
Design/methodology/approach
Using nonlinear econometric modeling, this paper investigates the oil market adjustment dynamics for four developed and emerging countries: France, the USA, Mexico and the Philippines. Our findings show strong evidence of significant linkages between oil and stock markets for all the countries under consideration.
Findings
As in Jawadi et al. who focus on stock price dynamics regarding oil price, the findings of this present paper, which focuses more on the oil industry, also point to an asymmetrical mean‐reversion between oil and stock markets that occurs in a nonlinear manner. They reject the informational efficiency hypothesis for oil markets. Indeed, while the previous literature often highlights the stock markets' dependence on the oil industry, this study contributes to the literature by concluding in favor of significant feedback from stock to oil markets, which is not compatible with the efficiency principle according to Fama.
Research limitations/implications
This paper develops a new nonlinear framework that should improve the investigation of oil‐stock market linkages. Future research could check the forecasting properties of this model to forecast the future dynamics of oil prices.
Originality/value
This paper adds to the literature by suggesting that it is not only oil shocks that affect stock markets, but that the latter also have a strong nonlinear impact on oil markets, reducing the diversification benefits of oil‐stock portfolios.
Interest has been growing in testing for nonlinearity and chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We apply five tests for nonlinearity or chaos to various monetary aggregate data series. We find that the inferences vary across tests for the same data, and within tests for varying sample sizes and various methods of aggregation of the data. Robustness of inferences in this area of research seems to be low and may account for the controversies surrounding empirical claims of nonlinearity and chaos in economics.
Modern economies have been subjected to a number of shocks during the past several years such as the burst of the Internet bubble, terrorist attacks, corporate scandals, the war in Iraq, the uncertainty about energy prices, and the recent subprime mortgage crisis. In particular, during the last few years, the energy shock has caused concerns for potential stagflation for both the United States and numerous other countries. We perform numerous univariate tests for non-linearity and chaotic structure using price data from the energy sector to resolve whether the sector's fundamentals or exogenous shocks drive these prices.
This paper uses a flexible approach to characterize the nonlinear relation between oil price changes and GDP growth. The paper reports clear evidence of nonlinearity, consistent with earlier claims in the literature—oil price increases are much more important than oil price decreases, and increases have significantly less predictive content if they simply correct earlier decreases. An alternative interpretation is suggested based on estimation of a linear functional form using exogenous disruptions in petroleum supplies as instruments.
In this paper, we discuss a number of univariate tests for independence and hidden nonlinear deterministic structure, and apply these tests to the Canadian exchange rate, using daily data over a 30-year period from January 2, 1973 to February 14, 2003.
Interest has been growing in testing for nonlinearity or chaos in economic data, but much controversy has arisen about the available results. This paper explores the reasons for these empirical difficulties. We designed and ran a single-blind controlled competition among five highly regarded tests for nonlinearity or chaos with ten simulated data series. The data generating mechanisms include linear processes, chaotic recursions, and non-chaotic stochastic processes; and both large and small samples were included in the experiment. The data series were produced in a single blind manner by the competition manager and sent by e-mail, without identifying information, to the experiment participants. Each such participant is an acknowledged expert in one of the tests and has a possible vested interest in producing the best possible results with that one test. The 2000 observation case was large enough to support the use of asymptotic inference, and (3) the inclusion of a noisy chaotic case. But the computational burdens upon the participants in this competition were already pressing the limits that could reasonably be expected of those courageous enough to subject their tests to this professionally risky competition.
This paper uses daily observations on West Texas Intermediate (WTI) crude oil prices at Chicago and Henry Hub natural gas prices at LA (over the deregulated period of the 1990s) and various tests from statistics and dynamical systems theory to support a random fractal structure for North American energy markets. In particular, this evidence is supported by the Vassilicos et al. (1993) multifractal structure test and the Ghashghaie et al. [Nature 381 (1996) 767] turbulent behavior test.
This paper presents a test of independence that can be applied to the estimated residuals of any time series model that can be transformed into a model driven by independent and identically distributed errors. The first order asymptotic distribution of the test statistic is independent of estimation error provided that the parameters of the model under test can be estimated [image omitted] -consistently. Because of this, our method can be used as a model selection tool and as a specification test. Widely used software1 written by Dechert and LeBaron can be used to implement the test. Also, this software is fast enough that the null distribution of our test statistic can be estimated with bootstrap methods. Our method can be viewed as a nonlinear analog of the Box-Pierce Q statistic used in ARIMA analysis.
While there is good reason to expect crude oil production to be non-linear, previous studies that have examined the stochastic properties of crude oil production have assumed that crude oil production follows a linear process. If crude oil production is a non-linear process, conventional unit root tests, which assume linear and systematic adjustment, could interpret departure from linearity as permanent stochastic disturbances. The objective of this paper is to test for non-linearities and unit roots in crude oil production. To realize our objective, this study applies a threshold autoregressive model with an autoregressive unit root to monthly crude oil production for 17 OPEC and non-OPEC countries over the period January 1973 to December 2007. Specifically, first we test for the presence of non-linearities (threshold effects) in the production of crude oil in two regimes. Second, we test for a unit root against a non-linear stationary process in two regimes and a partial unit root process when the unit root is present in one regime only. We find that crude oil production is characterized by threshold effects. We find that for eleven of the countries a unit root was present in both regimes, while for the others a partial unit root was found to be present in either the first regime or second regime.
The authors show that modifying the standard neoclassical growth model by assuming that competition is imperfect makes it easier to explain the size of the declines in output and real wages that follow increases in the price of oil. Plausibly parameterized models of this type are able to mimic the response of output and real wages in the United States. The responses are particularly consistent with a model of implicit collusion where markups depend positively on the ratio of the expected present value of future profits to the current level of output. Copyright 1996 by Ohio State University Press.
This paper employs response surface regressions based on simulation experiments to calculate distribution functions for some well-known unit root and cointegration test statistics. The principal contributions of the paper are a set of data files that contain estimated response surface coefficients and a computer program for utilizing them. This program, which is freely available via the Internet, can easily be used to calculate both asymptotic and finite-sample critical values and P-values for any of the tests. Graphs of some of the tabulated distribution functions are provided. An empirical example deals with interest rates and inflation rates in Canada. Copyright 1996 by John Wiley & Sons, Ltd.
A statistical test based on the estimated bispectrum is presented, which can distinguish between the linear stochastic dynamics widely used in macroeconomic models and alternative nonlinear dynamic mechanisms, including both nonlinear stochastic models and nonlinear deterministic (chaotic) models. The test is applied to an aggregate stock market index and to an aggregate industrial production index. In both cases, the test easily rejects the null hypothesis of a linear stochastic generating mechanism. This result strongly suggests that nonlinear dynamics (deterministic or stochastic) should be an important feature of any empirically plausible macroeconomic model. Copyright 1989 by Economics Department of the University of Pennsylvania and the Osaka University Institute of Social and Economic Research Association.
Traditional econometric models assume a constant one-period forecast variance. To generalize this implausible assumption, a new class of stochastic processes called autoregressive conditional heteroscedastic (ARCH) processes are introduced in this paper. These are mean zero, serially uncorrelated processes with nonconstant variances conditional on the past, but constant unconditional variances. For such processes, the recent past gives information about the one-period forecast variance. A regression model is then introduced with disturbances following an ARCH process. Maximum likelihood estimators are described and a simple scoring iteration formulated. Ordinary least squares maintains its optimality properties in this set-up, but maximum likelihood is more efficient. The relative efficiency is calculated and can be infinite. To test whether the disturbances follow an ARCH process, the Lagrange multiplier procedure is employed. The test is based simply on the autocorrelation of the squared OLS residuals. This model is used to estimate the means and variances of inflation in the U.K. The ARCH effect is found to be significant and the estimated variances increase substantially during the chaotic seventies.
This article applies a newly developed statistical technique to time series of daily rates of return of 15 common stocks. The technique involves estimating the bispectrum of the observed time series. The bispectrum is defined as the double Fourier transform of the third-order cumulant function. If the process generating rates of return is linear with independent innovations, then the skewness of the bispectrum will be constant. The article describes a test that can detect nonconstant skewness in the bispectrum. Hence if the test rejects constant skewness, a nonlinear process is implied. As a consequence, the test can distinguish between white noise and purely random noise. The results suggest that daily stock returns are generated by a nonlinear process.
The macroeconomics of oil shock
- Sill
Detecting Epochs of Transient Dependence in White
- M J Hinich
- D M Patterson