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Trends And Random Walks In Macroeconomic Time Series: Further Evidence From A New Approach
Abstract
This paper presents a summary of recent work on a new methodology to test for the presence of a unit root in univariate time series models. The stochastic framework is quite general. While the Dickey-Fuller approach accounts for the autocorrelation of the first-differences of a series in a parametric fashion by estimating additional nuisance parameters, this new approach deals with this phenomenon in a nonparametric way. We apply these new tests to reassess recent findings on the behavior of common macroeconomic time series, including the various series studied by Nelson and Plosser (1982).
... An interesting alternative proposed in Silva Lopes (2016) is to use the ADF test without linear time trend. This idea takes advantage of the results in Perron (1988), Campbell and Perron (1991) showing that the ADF test with only an intercept in the set of deterministic regressors has power that goes to zero (as the sample size T increases) in case the output gap is a trend stationary process. Thus, under trend stationarity, the ADF test does not (wrongly) reject the null of unit root. ...
... This author takes advantage of the results in Perron (1988), Campbell and Perron (1991) to exploit the fact that the ADF test with only an intercept in the set of deterministic regressors has power that goes to zero as the sample size increases in case the output gap is a trend stationary process. Thus, under trend stationarity, the ADF test does not (wrongly) reject the null of unit root, which makes unnecessary the second step of Pesaran (2007). ...
This paper proposes a novel test for the hypothesis of economic convergence. We extend the standard definition of convergence based on the parity condition and say that two economies converge if the time series of economic output are positively cointegrated and cotrended. With this definition in place, our main contribution is to propose a test of positive cointegration that does not require estimation of the cointegrating relationship, but is able to differentiate between positive and negative cointegration. Once the possibility of positive cointegration is established in a first stage, we test for cotrending in a second stage. Our sequential proposal enjoys an excellent performance in small samples due to the fast convergence of our novel test statistic under positive cointegration. This is illustrated in a simulation exercise where we report clear evidence showing the outperformance of our proposed method compared to existing methods in the related literature that test for economic convergence using cointegration methods. The results are particularly strong for sample sizes between 25 and 50 observations. The empirical application testing for economic convergence between the G7 group of countries over the period 1990–2022 confirms these findings.
... Alternatively, the Phillips Perron approach (PP), Phillips (1987) and Phillips and Perron (1988), allows for the presence of unknown forms of autocorrelation and conditional heteroscdasticity in the error term. Perron (1988) demonstrates that if a series is stationary about a linear trend but no allowance for this is made in the construction of the unit root test, then the probability of a type II error will be high. Thus, Perron (1988) suggests estimating the following regression by ordinary least squares, ...
... Perron (1988) demonstrates that if a series is stationary about a linear trend but no allowance for this is made in the construction of the unit root test, then the probability of a type II error will be high. Thus, Perron (1988) suggests estimating the following regression by ordinary least squares, ...
الدراسات والبحوث الإحصائية المطبقة على الطلب على النقود تهتم بالعلاقة التبادلية بين النقود والأدوات المالية وتأثير ذلك على الاحتفاظ بالأوراق المالية، و تطورات أسواق رأس المال والابتكارات المالية. ولكن توضح بعض الدراسات أن حركة أسعار الأسهم يمكن أن تؤثر على الطلب على النقود من ناحيتين: تأثير الثروة والتأثير التبادلي. وقد أدى تأسيس السوق السعودية للاسهم وتنظيمها وتطورها السريع إلى لفت انتباه القطاع الخاص، ودفعه للمشاركة الفعلية في التداولات في هذا السوق. باستخدام بيانات إحصائية ربع سنوية، هذه الدراسة تحاول أن تستقصي مدى وجود علاقة طويلة الأجل بين الطلب على النقود والأسعار الحقيقية للأسهم في المملكة. وباستخدام الطرق الحديثة في الاقتصاد القياسي توضح النتائج التي تم التوصل إليها أن ارتفاع أسعار الأسهم يؤثر على الطلب على النقود (خصوصاً M2) عن طريق الزيادة في النقود المخصصة للتعاملات, التأثير المباشر لعامل الثروة. أيضا قد يظهر التأثير التبادلي الذي يخفض الطلب على النقود، أي على أمكانية تحويل هذه النقود إلى أدوات مالية لها مردود. لهذا, فإنه يمكن استنتاج بأن دالة الطلب على النقود يجب أن تحتوي أسعار الأسهم الحقيقية بوصفها أحد المتغيرات المهمة في تحديد الطلب على النقود.
... In this part, the temporal properties of the variable used in this study will be tested using panel unit root tests such as Augmented Dickey-Fuller (ADF), Phillip Perron (PP), Im, Pesaran, and Shin (IPS), and Levin, Lin, and Chu (LLC) (Harris, 1992;Im et al., 2003;Levin et al., 2003, Perron, 1988. The rule of thumb is that if the absolute p-value for an LLC test, IPS test, ADF test, or PP test is less than 5 per cent of the critical value, the tested variable will be considered stationary or not contain a unit root. ...
The purpose of this work is to study Okun's law in a sample of North African economies (Algeria, Tunisia, Morocco, Libya, and Egypt) by examining the impact of the output gap on the unemployment gap and contributing to economic growth to reduce unemployment. These investigations aim to fill a significant gap in the empirical literature on the motives of Okun law in developing countries in general and North African countries in particular. The panel nonlinear ARDL model was used to examine the presence of Okun's law in North African economies over the period 1991-2023. The results of testing Okun's law in the sample of selected countries showed that Okun's law is valid for North African countries but in smaller amounts than those reached by Okun (between -2 and -3). Algeria recorded the highest value of -0.36. In addition, it was noted that the negative impact of GDP on unemployment rates is more significant than the positive impact in all the countries under study and is more critical in the cases of Algeria and Egypt. The study recommends prioritising economic growth through investments in labour-intensive sectors such as agriculture and industry, reducing bureaucratic inefficiencies, combating corruption, and fostering a favourable investment climate. Moreover, actions that can be taken involve improving training initiatives and implementing policies that promote the sector to stimulate the growth of stable employment opportunities. As a result, these empirical research findings regarding Okun’s Law are essential in shaping nations' economies and offer actionable suggestions for policymakers.
... Secondly, a general F-test based on Wald statistics is executed for each primitive variable (firstorder lagged). Moreover, the determined critical values from the F-statistics from the model of conditional error correction ARDL contingent at the bounds test of cointegration are applied as a final point to define the long-term relationship between the factors used in the study models [216], rendering results for the model of ARDL cointegration estimation (shown in Tables 6 and 7), and establishing that the standards of the F-Test Statistics are more significant than the upper limit at both the 1% significance level for Models 5, 6, and 8, and at the 5% significance level for Model 7, indicating that there is the cointegration between variables is in the long term of all of the study's models, which is consistent with the study of [206]. Notes: Table 6 presents the results of the ARDL bounds test. ...
The availability of agricultural land is central to stimulating reserves in sustainable food and crop production amidst accelerating economic sustainability and growth. Therefore, this article aims to investigate the influence of agricultural land (AGL) on food production (FP) and crop production (CP) with the linkage of environmental sustainability (ES) as a moderator from 1990 to 2021 for the economy of China with the autoregressive distributed lag (ARDL) bounds testing estimation model. Our findings showed that the ARDL model estimates the long-term and short-term joint matching relationships between agricultural land and the independent variables in the model, which is a statistically significant outcome. Therefore, in the long term, the food and crop production adjustment for speed to steadiness was huge as it was projected at 1.337%, 53.6%, 133.5%, and 37.4%, respectively, in all the models, which shows that the adjustment for speed of models is a good post-shock association process. We found evidence for a significant and positive relationship between agricultural land and food and crop production in ordinary least square (OLS) estimation, which also ensured the outcomes of the primary model. Furthermore, Toda–Yamamoto Granger causality test estimation found reverse causality between food production (FP) and crop production (CP) and showed evidence of the conservation hypothesis. We found bidirectional causality between food production and agricultural land and between crop production and agricultural land, which shows evidence of the feedback hypothesis. Additionally, the empirical findings of a robustness check with fully modified ordinary least square (FMOLS) and dynamic ordinary least square (DOLS) techniques showed consistency with the investigations of ARDL estimation in the long run, ensuring the validity and strength of the primary outcomes. Overall, the present paper brings fresh knowledge about agricultural land use, and food and crop production to promote environmental sustainability.
... In contrast, stationarity implies that a variable reverts to its mean over time. Several widely used methodologies assess stationarity, including the Augmented Dickey-Fuller (ADF) test (Dickey and Fuller 1981), the Phillips-Perron (PP) test (Perron 1988), the Levin, Lin, and Chu (LLC) test (Levin et al. 2002), and the Im, Pesaran, and Shin (IPS) test (Im et al. 2003). These tests differ in their assumptions regarding cross-sectional dependence and structural breaks, providing complementary insights into the nature of the time series. ...
This study examines the impact of foreign direct investment (FDI) and trade openness on economic growth in nine European countries using World Bank data (1995–2021). The analysis employs the Pooled Mean Group (PMG) Autoregressive Distributed Lag (ARDL) model to capture both short- and long-run dynamics. The findings indicate that FDI has a positive short-term effect but a negative long-term impact on economic growth. Similarly, trade openness stimulates growth in the short run but exerts a negative influence in the long run. Gross fixed capital formation has no immediate effect on GDP per capita but contributes positively in the long term. Granger causality tests reveal a unidirectional relationship from GDP per capita to both trade openness and gross fixed capital formation, while a bidirectional relationship exists between gross fixed capital formation and trade openness. These findings suggest the need for balanced policy measures to maximize the benefits of FDI and trade openness while mitigating long-term risks. Policymakers should focus on strengthening domestic industries, enhancing economic resilience, and implementing strategies to improve the absorptive capacity of FDI to optimize its long-run contributions to growth.
... 6 We also make use of a procedure by Rossi (2005) to measure median half-life for data series that is likely to be highly persistent. Perron (1988) highlighted the problem of ignoring the underlying order of integration in the data when estimating the linear deterministic trend. He concluded that the correct specification of the trend function could be affected by the presence of a unit root. ...
This short paper examines two potent issues that affect coffee producers worldwide. First, we estimate whether the real price of coffee received by producers are declining over time, making the coffee growers worse off. Secondly, we estimate how long it takes for exogenous shocks to dissipate, so that farmers can be better informed to manage volatile coffee prices. We find no evidence of any prevalent declining trend, and the time taken for a price shock to dissipate by half can vary widely from 5 to 18 months for individual coffee prices.
... Hence the Null Hypothesis NH 1 : There is no normal distribution among the crude oil volatility index (OVX) on sample Energy indices in India, was rejected during the study period. Said and Dickey (1984), and Phillips-Perron (PP) Tests (Perron (1988), to assess the stationarity of the sample factors. It is to be noted that all the sample variables attained significant levels of 1%, 5% and 10%. ...
This study investigates the co-movement and causal relationships between crude oil volatility (measured by the OVX) and the returns of three Indian energy indices: BSE Oil and Gas, BSE Power, and CNX Energy. Employing statistical techniques such as descriptive statistics, ADF and Phillips-Perron unit root tests, OLS regression, and wavelet analysis, we examine the dynamic linkages between these variables. Our findings reveal a predominantly negative relationship between OVX and the returns of the analyzed energy indices. These insights provide valuable information for investors to make informed investment decisions, particularly considering the impact of weather conditions on energy markets. Furthermore, the findings offer valuable guidance for policymakers, investment analysts, and other market participants.
... The most commonly used tests for unit root testing are Augmented Dickey-Fuller (Said and Dickey, 1984), Phillips-Perron (Perron, 1988), kpps (Kwiatkowski et al., 1992) and Ljung-Box (Box and Pierce, 1970). In particular, the Ljung-Box test contrasts the null auto-correlation hypothesis of identically distributed Gaussian random variables, which is equivalent to test stationarity. ...
... Panel (b) results show the Augmented Dickey-Fuller (ADF) test (Dickey and Fuller, 1981) and Phillips-Perron (PP) test (Perron, 1988) for the daily returns of the TA-35 index and Tel-Bond 20 index. Results show that both ADF and PP values are highly significant, suggesting stationarity in TA-35 and Tel-Bond Index returns and stationarity in price levels. ...
Purpose
This study investigates the influence of trading mechanisms on cross-market integration between stocks and corporate bonds on the Tel Aviv Stock Exchange (TASE) during the COVID-19 crisis. Unlike the worldwide practice of trading corporate bonds on an over-the-counter ( OTC ) market, TASE uses a limit-order-book (LOB) for both stocks and bonds, potentially creating unique volatility dynamics through direct information spillover. We analyze the volatility dynamics and spillover effects between TASE’s stock and corporate bond markets.
Design/methodology/approach
We employ an exponential general autoregressive conditional heteroskedastic (EGARCH)(1,1) model to assess the impact of stock market fear, measured by implied volatility, on Tel-Bond 20 Index returns and volatility. A bivariate diagonal Baba-Engle-Kraft-Kroner (BEKK) model is also applied to capture time-series integration and cross-volatility spillovers between the TA-35 Index (stocks) and the Tel-Bond 20 Index (corporate bonds), especially during financial stress.
Findings
The EGARCH model reveals a significant contagion effect, with increased stock market fear lowering corporate bond returns and increasing bond volatility. It also indicates a leverage effect, where negative shocks disproportionately amplify bond volatility. Diagonal BEKK results confirm strong cross-market volatility persistence, especially during crises, highlighting substantial financial contagion between stocks and bonds in TASE. While TASE’s market design improves the overall market quality, these findings underscore the LOB trading mechanism in facilitating financial contagion and systemic risk.
Practical implications
The LOB trading in TASE facilitates direct information flow, intensifying volatility spillover and cross-market integration, with the degree of integration fluctuating based on market conditions. Investors and managers should consider alternative hedging strategies during volatile periods, as stock market sentiment significantly impacts bond stability. Regulators should assess how trading mechanisms affect market integration and risk, especially during periods of distress.
Originality/value
This study offers new insights into how trading mechanisms influence cross-market dynamics, contributing to the literature on market design and financial contagion.
... MZa, MZt, MSB ve MPT olarak adlandırılan çeşitli test istatistikleri sunmaktadır. Bunlar Perron (1988), Bhargava (1986) ve Elliot vd. (1996) tarafından geliştirilen testlerin geliştirilmiş versiyonlarıdır. ...
Bu çalışma finansal gelişme-yenilenebilir enerji kullanımı ilişkisini Türkiye ekonomisi örneğinde 1980-2020 dönemi için analiz etme amacı taşır. Çalışma ekonomik büyüme, teknolojik yenilik ve petrol fiyatını yenilenebilir enerji modeline ilave değişkenler olarak entegre eder. ARDL ve Toda-Yamamoto prosedürleri eşbütünleşme ve nedensellik analizleri için uygulanmaktadır. Bulgular ekonomik büyüme, finansal gelişme, teknolojik yenilik, petrol fiyatı ve yenilenebilir enerji kullanımı arasında bir eşbütünleşmeye işaret etmektedir. Bulgular finansal gelişme, ekonomik büyüme ve teknolojik yeniliğin yenilenebilir enerji tüketimi ile pozitif ilişkide olduğunu göstermektedir. Finansal gelişme ile yenilenebilir enerji tüketimi arasındaki nedenselliğin çift yönlü olduğu belirlenmektedir. Tüm ampirik sonuçlar politika yapıcıları için önemli eğilimler içermektedir.
... Having identified a breakpoint, we proceeded to check whether the estimated β's behave like a shift model (Model 3 and Fig. 1) by running a unit-root test on the residuals of Model 4. If the test rejects the null hypothesis of non-stationarity, our assumption holds: before and after the breakpoint (i.e., at different levels), the series are stationary. To assess non-stationarity, we used the PP test (Perron, 1988), which incorporates heteroskedasticity. ...
Between 1992 and 2007, the Italian healthcare system underwent a profound and complex transformation. This reform rekindled interest in the study of health and mortality inequalities in Italy, and fears were expressed that the new system could trigger a rise in health disparities across regions. We contribute to the debate examining the evolution of life expectancy across Italian regions from 1974 to 2019, focusing on regional convergence. Applying sigma- and beta-convergence analysis in a novel way, we detect structural breaks—marked trend variations—occurring shortly after the most significant policy reforms of the national health system, with stronger discontinuities among males. While not establishing any direct causal link, our findings suggest that the legislative changes of the period, focused on decentralizing responsibilities and management, may have halted the pre-existing trend towards homogenization and possibly opened up a new phase of re-emerging regional survival disparities.
... There are several panel unit root tests available, such as Augmented Dickey-Fuller (ADF) test [98], Phillip Perron (PP) test [99], Levin, Lin & Chu (LLC) test [100], and Im, Pesaran and Shin [101] (IPS) test [102]. The assessment of stationarity or the existence of unit roots is based on a comparison between the absolute p-value obtained from these tests and a significance threshold of either 0.01 or 0.05. ...
Southeast Asia's booming tourism and rapid economic growth create a unique setting to explore the interplay between economic development, tourism, and environmental sustainability. This study examines the complex interplay between tourism expansion, financial development, and environmental sustainability in Southeast Asia, specifically from 2000 to 2023. This research aims to fill gaps in previous studies, particularly within the Association of Southeast Asian Nations (ASEAN) context, and to provide a comprehensive understanding of how tourism and financial growth impact environmental outcomes in this region. The Autoregressive Distributed Lag (ARDL) model with Pooled Mean Group (PMG) specifications is utilized to analyze the long-term relationships between these factors while capturing the unique short-run dynamics of individual countries within Southeast Asia. The findings reveal intricate relationships spanning both short-term and long-term dynamics, highlighting the impact of tourism growth on environmental factors such as increased renewable energy use, Carbon Dioxide (CO 2) emission, and ecological footprints. One-way causality from tourism, financial development, and renewable energy use to the ecological footprint is observed, alongside bidirectional causality between various factors. Policy implications emphasize the need for sustainable tourism practices and renewable energy integration. This research location's specific focus on Southeast Asia provides critical insights for policymakers aiming to balance economic growth with environmental conservation.
... The null hypothesis of the test assumes there is existence of unit roots within the model where δ2 = 0. This study utilizes the Philips-Perron (1988) [27] test statistics. The unit root test results in table 2 indicates that annual manufacturing output is stationary variable at 5% significance level. ...
This study investigates the relationship between economic growth and fiscal decentralization considering the expenditure perspective using the vector error correction model (ECM) framework. The study also accounts for domestic credit, public debt, manufacturing output, and money supply. Unit root test is performed to determine the variable's integration order. Fiscal decentralization, domestic credit and economic growth are variables of integrated order one. A cointegration test is then performed to test for cointegration relationship. There exist a cointegration relation among economic growth, domestic credit and fiscal decentralization. There is a significant error correction term that is relatively low in the short term. In the long run, fiscal decentralization has a significant positive effect on economic growth. Finally, the Granger causality test is performed to determine the direction of the causal link. There exists a unidirectional causal flow from fiscal decentralization to economic growth. The introduction of devolved government unit as established by Kenya's 2010 constitution has led t o significant growth in economy development. There is therefore need to strengthen tax and monetary policies that will strengthen the new two-tier government structure.
... To analyze the data for each city, we used Eviews software with the Phillips and Perron test (PP test) to verify that the data is a stability time series [28]. In addition, we measured the skewness, kurtosis and standard deviation of the data for each city to give an indirect indication of the stability of the data. ...
With the rapid development of industry, haze pollution has become an urgent environmental problem. This study innovatively utilizes network-based methods to investigate the spatial correlation effects of haze pollution transmission between urban clusters in the Yangtze River Economic Belt. A spatial correlation network of haze pollution in the Yangtze River Economic Belt was constructed using 328 urban meteorological data collection points as research samples, and its structural characteristics were examined. Main findings are as follows: (1) The spatial correlation network of PM2.5 in the Yangtze River Economic Belt urban agglomeration exhibits typical network structural characteristics: obvious spatial correlation within the network. (2) Chengdu, Chongqing, Wuhan, Nanchang, Yichang, Changsha and Yueyang are located at the center of the spatial network. They have more receiving and sending relationships. (3) 36 cities can be divided into four types: bilateral overflow, net beneficiary, net overflow and broker. Each type has different functional characteristics and linkage effects in the network. (4) Haze pollution positively correlates with the city’s synergistic development capacity and urbanization rate, the higher the city’s development level and the higher the Urbanization rate, the stronger its haze pollution capacity. This study provides new insights into the study of the spatial correlation and impact of haze pollution.
... Accordingly, before the co-integration analysis, we opt to the unit roots testing of the concerned series. We emphasis on the common and widely used strategies such as ADF test proposed by Dickey and Fuller (1979) and the Phillips-Perron (PP) test developed by Phillips and Perron (1988) for judging the stationarity. However, for the small sample data, the former test (ADF) may lack efficiency due to its consideration only on the occurrence of the autocorrelation between variables. ...
There is a considerable debate on the impact of institutional quality including economic and political institutions on economic outcomes. Most of the existing discourse has focused only on their economic implications. This study, on the other hand, seeks to explore the role of market supporting institutions, measured by economic freedom, on environmental outcomes in Pakistan. While utilizing data for the period 2000–2020 and using ARDL bounds testing approach, we arrive at few important conclusions. The empirical results indicate that market supporting institutions such as economic freedom have strong negative impact on environmental degradation (measured by CO2 emissions per capita and CO2 emissions from electricity and heat production) in Pakistan. Importantly, the effect holds both in short-run as well as in the long-run, suggesting that the strength of market supporting institutions not only lowers environmental pollution in the country but it also mitigates the environmental degradation from electricity and heat production. The estimated results are robust through alternative estimation strategies. Ultimately, the study implies that the strength of market supporting institutions can be an eventual boon to the environmental outcomes of Pakistan’s economy.
... The null hypothesis of the test assumes there is existence of unit roots within the model where δ2 = 0. This study utilizes the Philips-Perron (1988) [27] test statistics. The unit root test results in table 2 indicates that annual manufacturing output is stationary variable at 5% significance level. ...
This study investigates the relationship between economic growth and fiscal decentralization considering the expenditure perspective using the vector error correction model (ECM) framework. The study also accounts for domestic credit, public debt, manufacturing output, and money supply. Unit root test is performed to determine the variable's integration order. Fiscal decentralization, domestic credit and economic growth are variables of integrated order one. A cointegration test is then performed to test for cointegration relationship. There exist a cointegration relation among economic growth, domestic credit and fiscal decentralization. There is a significant error correction term that is relatively low in the short term. In the long run, fiscal decentralization has a significant positive effect on economic growth. Finally, the Granger causality test is performed to determine the direction of the causal link. There exists a unidirectional causal flow from fiscal decentralization to economic growth. The introduction of a devolved government unit as established by Kenya's 2010 constitution has led to significant growth in economic development. Therefore, tax and monetary policies are needed to strengthen the new two-tier government structure.
... s e I e " e I a O teste da existência de relações estatísticas entre as variáveis é em geral feito em três passos. A análise inicial de qualquer série temporal deve passar pelos testes de estacionaridade (Dickey-Fuller, 1979,1981Perron 1988, Phillips e Perron 1988). Dada a natureza de cada série de dados, é pois necessário saber se cada uma das séries individualmente é ou não estacionária ou, dito de outra forma, saber qual a ordem de integração das variáveis. ...
Em Portugal, impera a visão de que o sector público é ineficiente, causador de má afectação de recursos, criando desincentivos vários e consequentemente, inibidor do crescimento económico. O objectivo deste trabalho é o de investigar, recorrendo à metodologia de cointegração e causalidade de Granger, até que ponto o papel do Estado em Portugal e em particular o peso do sector público (medido pelas despesas públicas) tem contribuído positiva ou negativamente para o crescimento económico português. Como primeira implicação destes resultados, resulta que os mesmos sustentam a linha de orientação da política económica dos últimos Governos, no sentido de reduzir o peso do Estado na economia portuguesa. Parece pois que as ineficiências do sector público português são importantes e que a inversão do ritmo de crescimento económico e a melhoria da produtividade podem de facto passar pela transferência de algumas actividades e funções do Estado para a iniciativa privada.
... The selection of appropriate methodologies for the investigation is dependent on factors like integration degree and stationarity qualities. The conclusions are drawn from studies utilizing the PP and ADF tests, respectively, conducted by Fuller and Hasza [44] and Perron [45], are presented in the results and discussion section. We look at the order in which we mix our study variables to practically investigate our research issues. ...
Although the existing literature on environmental sustainability (ES) emphasizes its importance, yet few empirical studies look at the major contributing variables to ES. Therefore, we examine how the use of renewable energy, globalization, and technological innovation (TI) contribute to ES, with the moderating influence of foreign aid, spanning the period from 1996 to 2019 in BRICS economies. For data analysis, we apply the ARDL methodology, revealing an adverse and substantial link among globalization, TI, and the consumption of renewable energy with ES. Additionally, we discover that foreign aid has a beneficial moderating effect on the association between ES, globalization, and TI. On the other hand, it is found that foreign aid has an adverse moderating impact on the link between renewable energy sources and ES. This research also yields crucial practical implications, offering in-depth insights for the design of more effective policies to foster economic growth.
... Phillips-Perron (PP) and Kwiatkowski-Phillips-Schmidt-and-Shin (KPSS) unit root tests (Dickey & Fuller, 1979;Kwiatkowski et al., 1992;Perron, 1988). ...
Objective: the current study aims to empirically examine the dynamic impacts of ecosystem, with a particular focus on some agricultural indicators such as agricultural value added, crop production index, and livestock production index on CO2 emissions using annual time series data from 1990 to 2021. In order to enhance agricultural practices and develop successful sustainable agriculture policies in Egypt's agriculture sector. Method: A literature review involving numerous studies has revealed that agriculture is a significant contributor to the emission of CO2 into the atmosphere, hence exacerbating the phenomenon of global warming. These studies utilized many methodologies, including ARDL, DOLS, FMOLS, CCR, and Johansen, to accomplish their objectives. These methodologies were applied to annual data from multiple countries. Therefore, this study used Johansen's cointegration test to fulfill their objectives. Results and Discussion: The findings indicate that a 1% rise in agriculture value added and crop production index is found to be associated with a long-run decrease in carbon dioxide emissions of around 0.48% and 0.78%, respectively. A bidirectional causal relationship existed between carbon dioxide emissions and livestock production. Additionally, livestock production has a causal effect on crop production and conversely, crop production influences livestock production. Research Implications: Enhancing agricultural productivity and environmental sustainability can be achieved by adopting climate-smart practices in the agriculture sector, at both local and global levels. Originality/Value: This research study makes a valuable contribution to the existing body of literature by examining the significant and causal connections between environmental degradation and agriculture in the long term. This research demonstrates its significance and worth through its potential to aid policymakers in Egypt and other developing countries in formulating and executing efficient policies designed to address environmental degradation.
... Além desses estudiosos, outros pesquisadores também se debruçaram sobre a temática, como: Brown et al. (1975), Dickey e Fuller (1979), Nelson e Plosser (1982), Perron (1988), Zivot e Andrews (1992), Perron e Vogelsang (1992). ...
Objective: Analyzing, by means of an AR model, the presence of structural breaks in the interest rate series and, as a result, to verify the effects and/or changes in the share price level of certain publicly traded companies broken down by economic sectors, from January 2015 to June 2022. Theoretical Framework: Monetary policy has a substantial effect on investment intentions and, consequently, this is reflected in the business environment channeled through the Brazilian market indicator, the Ibovespa. A structural break is when the trends and patterns of association between observations in a time series change. This break usually reflects difficult times, such as the COVID-19 pandemic. Method: Using an AR model and statistical tests, the presence of structural breaks in the Selic series was analyzed. The aim was to identify repercussions on the Brazilian stock market, for which the market value of 12 Ibovepa companies was used as a proxy. Results and Discussion: There was a divergence between the share price and the interest rate when the structural breaks occurred. Research Implications: Knowing these structural changes can improve forecasting capacity and reduce the risk of estimating erroneous results. Originality/Value: This study contributes to the literature by analyzing the accuracy of forecasts, verifying the magnitude of any shortfall, which can be used to make decisions in the business environment.
... Nelson and Plosser expound that a unit root in real output is uneven with the belief that business cycles are stationary variations all over a deterministic trend. Many prior studies including Perron (1988) endorse the findings of Nelson and Plosser (1982). ...
... Stationarity of the data is therefore determined using the following procedure. The outcomes of the stationarity tests using the Perron (1988), Dickey and Fuller (1979) and Lee and Schmidt (1996) tests are displayed in Hence, in light of the variables being integrated at order one (I(1)), it becomes necessary to examine the variables for cointegration in order to determine whether a long-run relationship exists subsequent to the determination of the lag length selection. ...
Investigating the correlation between digital financial services, mobile money usage, and money velocity in Ghana, the study analysed time series data spanning from 1992 to 2022. A composite index was constructed by principal component analysis using data extracted from the world development indicators, with the components mobile money usage, digital financial services, and velocity of money. The estimation utilised an impulse response function and vector error correction model; the results indicated that mobile money, digital financial services, and money velocity are related in both the short and long term. Furthermore, the application of a standard deviation innovation to the velocity of money produced increases of both positive and negative magnitude for all the variables. This suggests that mobile money, digital banking services, and velocity of money in Ghana are interdependent in an asymmetric manner. In order to facilitate an increase in the velocity of money, the research concluded that policymakers should guarantee that a greater proportion of the population has access to mobile money and digital banking services. In addition to promoting mobile money, online banking services, and digital payment methods on purpose, the government should reduce reliance on physical currency and expedite the circulation of money. It is recommended that future longitudinal studies involving African nations employ diverse estimation techniques.
... By incorporating it into the analysis, researchers can determine the appropriate lag duration that ensures the error term's distinctiveness. Following the ADF test, this study uses the Phillips-Perron unit root test, where the former test has been improved by Phillips (1987) and Perron (1988). The distinction between the two frameworks lies in the Phillips-Perron arrangement accommodates a broad range of error structures, which can exhibit autocorrelation and heterogeneity in their distribution. ...
In contemporary times, geopolitical risk, and natural resources prices are susceptible due to the Russian-Ukraine conflict. In the meantime, emerging economies are struggling to explore the factors that could reduce ecological challenges and enhance environmental management. This research aims to analyze several economic, environmental , political, and institutional variables to ascertain their influence on greenhouse gas emissions in China. Covering the latest period from 1990 to 2022, various time series tests, including normality, stationarity, and cointegration tests. The results confirm that the variables studied have a stable pattern over time and are connected in the long run. The non-normal distribution of variables leads to opt novel moment quantile regression, where the results are tested for robustness via parametric approaches. The empirical results asserted that economic growth, natural resource prices, and trade significantly enhance ecological challenges (emissions). However, globalization, geopolitical risk, and institutional quality significantly reduce such environmental challenges. The results are robust, and both unidirectional and bidirectional causal associations confirm the importance of these variables in environmental management. Based on the results, this study recommends engagement in environmentally-friendly trading, investment in clean and green energy, and strengthening institutional quality for the region's environmental recovery.
... Uncertainty surrounding the deterministic mean function and the initial conditions is also known to affect the tests' performance [14,29,47] and, moreover, make the assumptions of standard testing procedures unlikely to be met. Various strategies for dealing with these types of uncertainty have been suggested for non-seasonal unit root tests, including sequential pre-testing for trend specifications and unit roots, data-dependent weighted averaging of unit root tests and running unionof-rejections decision rules [1,22,35]. Although these strategies may involve multiple tests, they usually work with only a small pre-selection of tests, often from the same family. ...
There is a wide variety of non-seasonal and seasonal unit root tests. However, it is not always obvious which tests can be relied upon due to uncertainties in identifying the data generating process, often with respect to the presence of deterministic terms and the initial conditions. We evaluate the size and power of a large set of unit root tests on time series that are simulated to be representative of economic time series in the M4 competition data. Furthermore, using a conditional random forest-based elimination algorithm, we assess which tests should be combined to improve the performance of each individual test.
... For testing the stationarity of the data, we used in this study verity panel unit root tests such as the augmented Dickey-Fuller (ADF) [72], Phillips-Perron (PP) [73], Levin and Zhang [74] (LLC), and Mitić et al. [75] (IPS). Thus, if the absolute P values of these tests are less than 5 percent critical value, it means that the tested variable does not have unit root or stationary. ...
The paper investigates the interplay between clean energy, environmental pollution reduction, and economic growth in the Gulf Cooperation Council (GCC) countries from 1980 to 2019, utilizing the autoregressive distributed lag (ARDL) method. The study underscores the global transition towards cleaner energy sources and its implications for the region. In assessing the determinants of economic growth, the findings reveal a positive and significant short- and long-term impact of energy production, with energy consumption exhibiting a positive and significant effect solely in the long term. The absence of a confirmed relationship in the short term is notable. Causality tests demonstrate a significant link from both energy consumption types to environmental pollution, alongside causal relationships from urbanization, energy production, and consumption to economic growth. Moreover, the results include the pivotal role of energy production in driving GDP growth, caution in short-term energy consumption effects, and significant causal links between energy consumption and environmental pollution. The recommendations to incentivize sustainable energy production, engage in long-term energy consumption planning, and adopt integrated urbanization policies provide actionable insights for policymakers. These suggestions are aimed at guiding the GCC countries in balancing the pursuit of economic growth with environmental sustainability—a delicate equilibrium that necessitates careful consideration of various factors.
... According to the classic econometric text book, one of the assumptions in estimating a regression model is that all variables must be stationary. According to research, the bulk of macroeconomic time series variables are stationary in terms of their levels or first-differences (Nelson & Plosser, 1982;Perron, 1988). The first-differences formula for calculating a variable logx t is Δlogx ¼ logðx t =x tÀ 1 Þ. Figure 3 depicts job loss, new cases, and new deaths in levels, as well as log changes (differences) in the job loss, new cases, and new deaths, as well as their unexpected logarithmic oscillations. ...
This study employs a suitable volatility model that examines the impact of COVID-19 new cases and deaths on the volatility of daily job loss in Malaysia. Autoregressive Distributed Lag (ARDL) and Generalized Autoregressive Conditional Heteroscedasticity (GARCH) were employed as the modelling strategy to estimate daily data from January to December 2020. In addition, the asymmetric GARCH-M (EGARCH-M, TGARCH-M, and PGARCH-M) were further applied. The findings from different versions of the ARDL(p,q1,q2)-(E,T,P)GARCH(1,1)-M model show that the ARDL-EGARCH-M model can capture the volatility and clustering of variability in job loss. The findings revealed asymmetry effects, suggesting that negative shocks (bad news) in a pandemic period increased volatility in job loss compared to positive shocks (good news). Policy implications relating to lockdown measures and news signals were provided.
... Essa classificação considera as diversas densidades tecnológicas de saúde que estão disponíveis para a população no contexto nacional de saúde do Brasil (24) . (28)(29)(30) . Com esta avaliação, os parâmetros de entrada utilizados na função auto.arima ...
Objetivo: analisar o padrão temporal e estimar as taxas de mortalidade nas primeiras 24 horas de vida e por causas evitáveis no estado de Pernambuco no período de 2000 a 2021. Método: estudo ecológico, tendo como unidade de análise o trimestre. A fonte de dados foi constituída pelo Sistema de Informações sobre Mortalidade e pelo Sistema de Informações sobre Nascidos Vivos. A modelagem da série temporal foi conduzida segundo o Modelo Autorregressivo Integrado de Médias Móveis. Resultados: foram registrados 14.462 óbitos nas primeiras 24 horas de vida, sendo 11.110 (76,8%) evitáveis. Observa-se para os forecasts que a taxa de mortalidade nas primeiras 24 horas de vida variou de 3,3 a 2,4 por 1.000 nascidos vivos, e a taxa de mortalidade por causas evitáveis variou de 2,3 a 1,8 por 1.000 nascidos vivos. Conclusão: a previsão sugeriu avanços na redução da mortalidade nas primeiras 24 horas de vida no estado e por causas evitáveis. Os modelos ARIMA apresentaram estimativas satisfatórias para as taxas de mortalidade e por causas evitáveis nas primeiras 24 horas de vida.
... Para definir los parámetros de entrada de la función auto.arima, se evaluaron las funciones de Autocorrelación (ACF) y Autocorrelación Parcial (PACF) así como las pruebas de Estacionariedad Aumentada de Dickey-Fuller (ADF), Phillips-Perron (PP) y Kwiatkowski-Phillips-Schmidt-Shin (KPSS)(28)(29)(30) . Con esta evaluación, los parámetros de entrada utilizados en la función auto. ...
Objective:
to analyze the temporal pattern and estimate mortality rates in the first 24 hours of life and from preventable causes in the state of Pernambuco from 2000 to 2021.
Method:
an ecological study, using the quarter as the unit of analysis. The data source was made up of the Mortality Information System and the Live Birth Information System. The time series modeling was conducted according to the Autoregressive Integrated Moving Average Model.
Results:
14,462 deaths were recorded in the first 24 hours of life, 11,110 (76.8%) of which being preventable. It is observed from the forecasts that the mortality rate in the first 24 hours of life ranged from 3.3 to 2.4 per 1,000 live births, and the mortality rate from preventable causes ranged from 2.3 to 1.8 per 1,000 live births.
Conclusion:
the prediction suggested progress in reducing mortality in the first 24 hours of life in the state and from preventable causes. The ARIMA models presented satisfactory estimates for mortality rates and preventable causes in the first 24 hours of life.
... It's akin to saying that the initial difference in the variable forms a series, suitable for application of the mean model. This simple benchmark demonstrated competitive performance in many scenarios, especially in time series that demonstrate random walk properties (Hewamalage, Ackermann, and Bergmeir 2023) Despite its inherent simplicity, the persistence model is broadly adopted across diverse fields for energy demand and price modelling (Löhndorf and Wozabal 2023), as well as in macroeconomic time series (Perron 1988), financial markets (Black and Scholes 1973), and even fundamental sciences, including physics (Risken and Voigtlaender 1984), chemistry (Van Kampen 1992), material science (Doi and Edwards 1988), and biology (Goel and Richter-Dyn 2016). Marquez and Coimbra (2011) demonstrate the use of the persistent model for global and direct irradiance forecasting, and Paulescu and Paulescu (2019) used the persistent model to benchmark various statistical techniques. ...
This paper considers two pertinent research inquiries: ‘Can an AI-based predictive framework be utilized for the optimisation of solar energy management?’ and ‘What are the ways in which the AI-based predictive framework can be integrated within the Smart Grid infrastructure to improve grid reliability and efficiency?’ The study deploys a Deep Learning model based on Long Short-Term Memory techniques, leading to refined accuracy in solar electricity generation forecasts. Such an AI-supported methodology aids power grid operators in comprehensive planning, thereby ensuring a robust electricity supply. The effectiveness of this framework is tested using performance metrics such as MAE, RMSE, nMAE, nRMSE, and R2. A persistent model is utilised as a reference for comparison. Despite a slight decrease in predictive precision with the expansion of the forecast horizon, the proposed AI-based framework consistently surpasses the persistent model, particularly for horizons beyond two hours. Therefore, this research underscores the potential of AI-based prediction in fostering efficient solar energy management and enhancing Smart Grid reliability and efficiency.
... The Z-score follows an ex-post stochastic analysis, which is a relevant and useful approach to address issues of serial correlation and time-dependent heteroscedasticity (Agarwal & Taffler, 2007;Perron, 1988 andSharma &Dhakal, 1994). A Z-score is the outcome of the difference between a score and the mean of the scores divided by the standard deviation for the scores. ...
Purpose
An intractable effect of revenue and expense recognition based on tax regulation and accounting rules is unresolved and may be manageable only by reducing the value of deferred taxes. Therefore, in this study, the authors examined the relationship between the International Accounting Standard 12 (IAS 12) and deferred income taxes associated with tax and accounting rules.
Design/methodology/approach
The authors used a large sample of balanced data from 144 firms across 1992–2019. To mitigate the problem of superfluous results, the authors used the same number of firms and years for pre- and post-IAS 12 periods. The authors employed robust econometric estimations to establish the impact of IAS 12 on deferred tax.
Findings
The regression results show that deferred tax assets decreased significantly, whereas deferred tax liabilities increased significantly, in the post-IAS 12 period. These contrasting results imply that IAS 12 implementation has increased conservatism and prudence in financial reporting. However, the authors find that the increase in deferred tax assets post-IAS 12 is value destructive, suggesting that its implementation has unintended consequences. The results are robust to alternative measurements and econometric identification strategies.
Originality/value
While prior studies have explored topics such as deferred tax measurement and the impact of income and expense recognition, the authors specifically analyzed how IAS 12 affects deferred taxes and their effect on the market valuation. The authors find that certain accounting standards may not be relevant to the capital market.
... Complexityindicate that all those variables are not normally distributed, confrming the essentiality of quantile regression. At last, the results of the Augmented Dickey-Fuller (ADF) test[93,94], Phillips-Perron (PP) test[95], and Elliott, Rothenberg, and Stock's GLS version of the Dickey-Fuller (DF-GLS) test[96] by the last three columns indicate that the SPOT interest rate, the S&P 500 index, and the WTI oil price are nonstationary in levels but stationary in frst diference. Tus, to avoid the spurious regression issue, we frst apply diferencing to the control variables including the SPOT interest rate, the S&P 500 index, and the WTI oil price. ...
Previous studies focused on the fundamental channels of the interaction between the equity market and credit default swap (CDS) market. This paper finds another channel, investor sentiment, that contributes to the impact of the equity market on the CDS market under different time horizons and market conditions within the framework of wavelet quantile regression. It absorbs both the merits of wavelet transform and quantile regression and is advantageous in analyzing heterogeneous time horizons and full conditional distributions. Empirical results show that investor attitude turning optimistic has a negative influence on the deviation of CDS market spread from theoretical value, while the intensification of fear among equity market will enlarge this deviation. Besides, we discovered that the influence of equity market sentiment on the CDS market first increases and then decreases as the time horizon lengthens and that the greater the deviation of CDS spreads from intrinsic value is, the more irrational the CDS market participants are. These findings suggest that the influence of investor sentiment on the credit default swap market is self-reinforced. Our results are robust after controlling for macroeconomic conditions and under different wavelet decompositions. Reasonable suggestions are given to financial institutions, investors, and policy makers based on our findings.
... Suppose 1 ≠ 0 but the time trend regressor, t, is left out of (1) or (2a). Then it is well known (Perron, 1988) that the ADF unit root test will suffer 150 from systematically low power (biased toward non-rejection when the series is trend stationary). ...
The standard trend model for measuring climate warming assumes error terms are mean-reverting and stationary. But the climate econometrics literature has argued that if anthropogenic forcing is a dominant driver of climate, temperature trends must have nonstationary (unit root) error terms, which may be considered a “fingerprint” for anthropogenic forcing. Herein we explain this paradox and apply some tools from time series econometrics to resolve it. We formalize a previously proposed hypothesis for why past results have been unclear, namely that temperatures contain both a nonstationary forcing component and a stationary “weather noise” component that may bias unit root tests towards over-rejection. Our analysis yields a diagnostic method for assessing whether this problem matters in practice. We apply unit root tests to observed and modeled temperature series at surface and tropospheric layers. We find observed temperatures are stationary around a trend after allowing for a single structural break in trend, with no evidence of testing bias due to weather noise. Unit root tests applied to model-generated temperatures also indicate trend stationarity however we find evidence of testing bias due to weather noise. This implies that time series models for climate attribution need to deal carefully with the requirements for establishing cointegration. We discuss the implications for understanding the relationship between greenhouse gas forcing and atmospheric temperatures over time.
... Available unit root tests and their applications are numerous. For example, Nelson and Plosser (1982), Stock and Watson (1986), Perron (1988), Evans (1989), Stock (1991) Rudebusch (1993) Among frequently applied asymptotic tests, we indicate Dickey and Fuller (1979) test (DF) Fuller (1979) test which are considered for testing H 1 : m 1 = 1, |m j | < 1 ∀ j = 2, · · · , p, Hasza and Fuller (1979) (HF) test for testing H 2 : m 1 = m 2 = 1, |m j | < 1 ∀ j = 3, · · · , p. These asymptotic tests suer from weak power problem and size control problem;see Diebold and Nerlove (1990), DeJong, Nankervis, Savin and Whiteman (1992), Sen (1985), Dickey and Pantula (1987), DeJong et al. (1992), Kwiatkowski, Phillips, Schmidt and Shin (1992), Blough (1992), Leybourne and Newbold (1999), Ayat and Burridge (2000). ...
... Entre eles testes com taxa de verossimilhança de seleção de defasagens, 15 uso de R 2 corrigido e uso da estatística de Ljung-Box. Os resultados das estimações das equações reduzidas estão nas Tabelas 1 e 2. Perron (1988). 13 Mesmo que obtivéssemos através de testes que as duas variáveis do modelo são cointegradas não poderíamos impor essa restrição às estimações, pois essa cointegração deveria ser apenas por causa de circunstâncias fortuitas do período em que as séries foram definidas. ...
This paper suggests that antidumping clauses in the World Trade Organization could have a positive impact in the growth of Third World countries. The labor cost increases caused would pressure for faster technical change, accelerating growth. The possible short-term unbalances in the current accounts would be temporary and would vanish in the long-term. It is also argued that the political alliances to introduce such clauses in an international organization could be an important change in the world political scene, bringing hope of forthcoming prevailing international relations that could be more positive for Third World growth.
KEYWORDS:
International labor division; labor quality; antidumping
... Pedroni (1999) membahas pengembangan tujuh statistik panel kointegrasi; yaitu 4 berdasarkan pooling within dimension dan 3 berdasarkan pooling between dimension. Pada kategori pertama, 3 dari 4 pengujian mencakup penggunaan koreksi non-parametrik dari Philips- Perron (1988), sedangkan model keempat dengan parameter berdasar uji ADF. Pada kategori kedua, 2 dari 3 uji menggunakan koreksi non-parametrik, sementara kategori ketiga menggunakan uji ADF. ...
Penurunan produktivitas pekerja, yang terjadi dalam masa krisis, menjadi alasan bagi pengusaha untuk menurunkan upah nominal. Sementara itu, masa krisis juga menyebabkan penurunan upah riil akibat tingginya in asi sehingga pekerja menuntut kenaikan upah nominal guna mempertahankan kesejahteraannya. Studi ini menganalisis penentuan upah nominal pada industri kimia dalam masa krisis. Studi ini menggunakan alat analisis regresi berdasar model data panel dinamis. Hasil studi menunjukkan bahwa selama masa krisis, tingkat upah nominal tidak mengalami penurunan. Pengusaha menyatakan bahwa penurunan upah nominal berdampak negatif pada kinerja perusahaan. Dalam masa krisis, ketegaran upah nominal untuk turun merupakan sarana rekonsiliasi hubungan industrial.
... So, it is important to diagnose unit root problem because macroeconomic variables mostly have the problem of unit root or non-stationary nature. (Perron, 1988) suggested that the results will be misleading for economic analysis if OLS is treated non-stationary series. With significant t and F-statistics, high R-squared is created the problem of spurious regressions (Granger & Newbold, 1974). ...
This study analyzes the impacts of economic growth on ecosystem in Türkiye. The study uses annual data for the period 1995-2021 and the ARDL method. The study utilizes the Ecosystem Vitality Index, a sub-dimension of the Environmental Performance Index. In addition, seven models were constructed to assess in detail the impact of economic growth on different dimensions of the ecosystem. The results show that economic growth has a significant impact in all models analyzed. However, the direction of this impact differs across ecosystem components. Economic growth is found to have a positive impact on agriculture and water resources. In these models, a 1% increase in GDP increases the agriculture and water resources indices by 0.074-0.672%. In contrast, economic growth has a negative impact on biodiversity and habitat, ecosystem services, fisheries, acid rain and total ecosystem vitality. In these models, a 1% increase in GDP reduces the indices of biodiversity and habitat, ecosystem services, fisheries, acid rain and total ecosystem vitality by 0.101-2.144%. The results suggest that the environmental costs of economic growth processes need to be considered. Environmentally friendly policies should be combined with sustainable development strategies to reduce the negative impacts of economic growth.
This study aims to assess the relationship between economic growth, renewable energy consumption, and sustainable development in the BRICS countries, addressing the complex dynamics and policy implications of achieving green growth. By Utilizing a panel data approach, this research employs the Panel Autoregressive Distributed Lag (ARDL) model to explore both short-term and long-term relationships among GDP growth, CO2 emissions, renewable energy consumption, quality of education, and zero hunger initiatives from 2010 to 2022. The study also used correlation matrix, ADF panel unit root tests and co-integration analyses to ensure the robustness of the findings. The results revealed a significant short-term positive relationship between GDP growth and CO2 emissions, and indicating that current economic activities in BRICS remain carbon-intensive to increase economic growth in short-term. However, in the long run, higher investments in the sectors of education and renewable energy notably reduces carbon emissions, showcasing their ability to foster sustainable development. The analysis further reveals a negative correlation between the consumption of renewable energy and CO2 emissions and a positive link between education spending and economic growth, underscoring the importance of human capital in driving sustainability. This study contributes to the existing literature by providing a comprehensive analysis of the socioeconomic impacts of green growth strategies in the BRICS countries. It underscores the necessity for integrated policies that balance economic advancement with environmental preservation and social inclusion. The findings offer valuable insights for policymakers to design effective strategies for achieving sustainable economic development in emerging economies.
This article deals with unit root issues in time series analysis. It has been known for a long time that unit root tests may be flawed when a series although stationary has a root close to unity. That motivated recent papers dedicated to autoregressive processes where the bridge between stability and instability is expressed by means of time‐varying coefficients. The process we consider has a companion matrix with spectral radius satisfying , a situation described as ‘nearly‐unstable’. The question we investigate is: given an observed path supposed to come from a nearly unstable process, is it possible to test for the ‘extent of instability’, i.e. to test how close we are to the unit root? In this regard, we develop a strategy to evaluate and to test for : ‘’ against : ‘’ when lies in an inner ‐neighborhood of the unity, for some . Empirical evidence is given about the advantages of the flexibility induced by such a procedure compared to the common unit root tests. We also build a symmetric procedure for the usually left out situation where the dominant root lies around .
This study assesses the influence of industrialization and energy consumption on the environmental sustainability for seven Asian emerging economies over the period 1990–2022 by using Panel ARDL estimation technique. Results show that industrialization adversely impacts environmental sustainability in the long run by discharging CO2, while energy consumption has a favourable environmental impact. In the short run, both factors have demonstrated overall as well as country specific adverse effects. Further, Dumitrescu Hurlin Panel causality results reported uni directional causal relationship moving from industrialization and energy consumption to carbon dioxide discharges. These results indicates that efforts of Asian emerging economies towards environmental sustainability are not sufficient. This study recommends policymakers consider different sustainability frameworks, increase awareness regarding adoption of environmental positive activities, and allocate more funding for environmental protection and technological innovation.
There is a wide variety of non-seasonal and seasonal unit root tests. However, it is not always obvious which tests can be relied upon due to uncertainties in identifying the data generating process, often with respect to the presence of deterministic terms and the initial conditions. We evaluate the size and power of a large set of unit root tests on time series that are simulated to be representative of economic time series in the M4 competition data. Furthermore, using a conditional random forest-based elimination algorithm, we assess which tests should be combined to improve the performance of each individual test.
Since the seminal paper of Nelson and Plosser (J Monet Econ 10(2):139–162, 1982), analyzing the nature of shocks to macroeconomic and financial data has attracted great attention and it continues to be up-to-date, especially, in conjunction with the advances in unit root literature. This paper examines the persistence in macroeconomic and financial variables for Turkey by means of the recent developments in the quantile autoregression models to account for non-normal distributions, structural changes, and asymmetric dynamics. The results show that while the conventional unit root approaches fail to reject the null hypothesis of unit root for most the of 30 macroeconomic and financial time series, the nonlinear quantile unit root test with smooth structural changes supports evidence on a stable long-run equilibrium for 23 variables. It further reveals asymmetric persistence in most of the Turkey’s macroeconomic and financial data, implying that the effect of an economic shock in inflationary state is different than that in recessionary state.
We design a ‘cascade model’ that integrates projections for Australian housing with inflation, incomes and asset markets over long horizons. The model allows simulating joint ‘paths’ for inflation, wages, cash rates, mortgage rates, rents, rental yields, house prices and fund returns. The cascade model structure ensures that equilibrium relationships are maintained between the variables when projecting over very long time periods. It achieves this through linking either growth rates or levels for variables in a manner that ensures consistent trends emerge within each simulated path over the very long‐term, thus avoiding excessively divergent behaviour between variables with common underlying fundamentals.
Objective: to analyze the temporal pattern and estimate mortality rates in the first 24 hours of life and from preventable causes in the state of Pernambuco from 2000 to 2021. Method: an ecological study, using the quarter as the unit of analysis. The data source was made up of the Mortality Information System and the Live Birth Information System. The time series modeling was conducted according to the Autoregressive Integrated Moving Average Model. Results: 14,462 deaths were recorded in the first 24 hours of life, 11,110 (76.8%) of which being preventable. It is observed from the forecasts that the mortality rate in the first 24 hours of life ranged from 3.3 to 2.4 per 1,000 live births, and the mortality rate from preventable causes ranged from 2.3 to 1.8 per 1,000 live births. Conclusion: the prediction suggested progress in reducing mortality in the first 24 hours of life in the state and from preventable causes. The ARIMA models presented satisfactory estimates for mortality rates and preventable causes in the first 24 hours of life.
There is a wide variety of non-seasonal and seasonal unit root tests. However, it is not always obvious which tests can be relied upon due to uncertainties in identifying the data generating process, often with respect to the presence of deterministic terms and the initial conditions. We evaluate the size and power of a large set of unit root tests on time series that are simulated to be representative of economic time series in the M4 competition data. Furthermore, using a conditional random forest-based elimination algorithm, we assess which tests should be combined to improve the performance of each individual test.
Traditionally, economic growth and business cycles have been treated independently. However, the dependence of GDP levels on its history of shocks, what economists refer to as “hysteresis,” argues for unifying the analysis of growth and cycles. In this paper, we review the recent empirical and theoretical literature that motivates this paradigm shift. The renewed interest in hysteresis (or “scarring” in recent parlance) has been sparked by the persistent impact of the global financial crisis —as GDP in advanced economies remained far below the precrisis trends for over a decade—and recent concerns about the lasting impact of the COVID-19 shock. The findings of the recent literature have far-reaching conceptual and policy implications. In recessions, monetary and fiscal policies need to be more active to avoid the permanent scars of a downturn. And in good times, running a high-pressure economy could have permanent positive effects. (JEL E22, E23, E24, E32, E63, G01, O41)
Let n observations Y 1, Y 2, ···, Y n be generated by the model Y t = pY t−1 + e t , where Y 0 is a fixed constant and {e t } t-1 n is a sequence of independent normal random variables with mean 0 and variance σ2. Properties of the regression estimator of p are obtained under the assumption that p = ±1. Representations for the limit distributions of the estimator of p and of the regression t test are derived. The estimator of p and the regression t test furnish methods of testing the hypothesis that p = 1.
This paper describes a theoretical and empirical study of the possibility of rational bubbles in the relative price ofgold. The critical implication of the theoretical analysis is that, if rational bubbles exist, the time series of the relative price of gold, as well as any time series obtained by differencing a finite number of times, is nonstationary. The empirical evidence relating to this nonstationarity property involves diagnostic checks for stationarity carried out in both the time domain and the frequency domain. This evidence strongly suggests that the process generating the first difference of the log of the relative price of gold is stationary, a finding that is inconsistent with the existence of rational bubbles. More broadly, the empirical analysis finds a close correspondence between the time series properties of the relative price of gold and the time series properties of real interest rates,which the theory relates to the time series properties of the fundamental component of the relative price of gold. In sum, the evidence is consistent with the combined conclusion that the relative price of gold corresponds to market fundamentals, that the process generating first differences of market fundamentals is stationary, and that actual price movements do not involve rational bubbles.
"Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street," observed legendary speculator Jesse Livermore. History tells us that periods of major technological innovation are typically accompanied by speculative bubbles as economic agents overreact to genuine advancements in productivity. Excessive run-ups in asset prices can have important consequences for the economy as firms and investors respond to the price signals, resulting in capital misallocation. On the one hand, speculation can magnify the volatility of economic and financial variables, thus harming the welfare of those who are averse to uncertainty and fluctuations. But on the other hand, speculation can increase investment in risky ventures, thus yielding benefits to a society that suffers from an underinvestment problem.
This paper studies the statistical properties of vector autoregressions (VAR's) for quite general multiple time series which are integrated of order one. Functional central limit theorems are given for multivariate partial sums of weakly dependent innovations and these are applied to yield first order asymptotics in nonstationary VAR's. Characteristic and cumulant functionals for generalized random processes are introduced as a means of developing a refinement of central limit theory on function spaces. The theory is used to find asymptotic expansions of the regression coefficients in nonstationary VAR's under very general conditions. The results are specified to the scalar case and are related to other recent work by the author in [17] and [19].
This paper studies the random walk in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984). Copyright 1987 by The Econometric Society.
[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
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.
This paper develops an asymptotic theory for a first-order autoregression with a root near unity. Deviations from the unit
root theory are measured through a noncentrality parameter. When this parameter is negative we have a local alternative that
is stationary; when it is positive the local alternative is explosive; and when it is zero we have the standard unit root
theory. Our asymptotic theory accommodates these possibilities and helps to unify earlier theory in which the unit root case
appears as a singularity of the asymptotics. The general theory is expressed in terms of functionals of a simple diffusion
process. The theory has applications to continuous time estimation and to the analysis of the asymptotic power of tests for
a unit root under a sequence of local alternatives.
This paper develops a general asymptotic theory of regression for processes which are integrated of order one. The theory
includes vector autoregressions and multivariate regressions amongst integrated processes that are driven by innovation sequences
which allow for a wide class of weak dependence and heterogeneity. The models studied cover cointegrated systems such as those
advanced recently by Granger and Engle and quite general linear simultaneous equations systems with contemporaneous regressor
error correlation and serially correlated errors. Problems of statistical testing in vector autoregressions and multivariate
regressions with integrated processes are also studied. It is shown that the asympotic theory for conventional tests involves
major departures from classical theory and raises new and important issues of the presence of nuisance parameters in the limiting
distribution theory.
Changes in variance, or volatility, over time can be modeled using the approach based on autoregressive conditional heteroscedasticity. Another approach is to model variance as an unobserved stochastic process. Although it is not easy to obtain the exact likelihood function for such stochastic variance models, they tie in closely with developments in finance theory and have certain statistical attractions. This article sets up a multivariate model, discusses its statistical treatment, and shows how it can be modified to capture common movements in volatility in a very natural way. The model is then fitted to daily observations on exchange rates.
This paper considers a Gaussian first-order autoregressive process with unknown intercept where the initial value of the variable is a known constant. Monte Carlo simulations are used to investigate the sampling distribution of the t statistic for the autoregressive parameter when its value is in the neighborhood of unity. A small sigma asymptotic result is exploited in the construction of exact non-similar tests. The powers of non-similar tests of the random walk and other hypotheses are estimated for sample sizes typical in economic applications.
A Lagrange multiplier test is derived for testing for the order of differencing in an autoregressive integrated moving average (ARIMA) model. The procedure is illustrated with an example.
Recently, methods for detecting unit roots in autoregressive and autoregressive-moving average time series have been proposed. The presence of a unit root indicates that the time series is not stationary but that differencing will reduce it to stationarity. The tests proposed to date require specification of the number of autoregressive and moving average coefficients in the model. In this paper we develop a test for unit roots which is based on an approximation of an autoregressive-moving average model by an autoregression. The test statistic is standard output from most regression programs and has a limit distribution whose percentiles have been tabulated. An example is provided.
This paper derives expressions for the exact bias and variance of a general class of spectral density estimators at the zero frequency, building on the work of Neave (The exact error in spectrum estimates. Ann. Math. Statist. 42 (1971), 961–75) who studied the case where the mean of the series is assumed known. These expressions are evaluated for 15 different windows and for a wide variety of stationary time series. The exact error of the estimators is found to depend on whether the sample mean has to be estimated, and some windows are noticeably inferior at certain values of the bandwidth. A response surface analysis reveals that the finite sample relationships between the bandwidth and the exact error are quite different from the ones suggested by asymptotic theory.
We Tabulate the Limiting Cumulative Distribution and Probability Density Functions of the Least Squares Estimator in a First-Order Autoregressive Regression When the True Model Is Near-Integrated in the Sense of Phillips (1986 A). the Results Are Obtained Using an Exact Numerical Method Which Integrates the Appropriate Limiting Moment Generating Function. the Adequacy of the Approximation Is Examined by Monte Carlo Methods for Various First-Order Autogressive Processes with a Root Close to Unity.
Under a modest generalization of the dynamics permitted for variables which are seen by agents but not the econometrician, many of the existing tests for the presence of speculative bubbles are not statistically valid. Less restrictive tests lead us to concur with Flood and Garber that speculative bubbles were not part of the German hyperinflation, but dispute Shiller's conclusion that stock prices are excessively volatile. Moreover, all such tests are subject to the admonition that what appears to be a speculative bubble could instead have arisen from rational agents responding solely to economic fundamentals not observed by the econometrician.
This paper investigates whether macroeconomic time series are better characterized as stationary fluctuations around a deterministic trend or as non-stationary processes that have no tendency to return to a deterministic path. Using long historical time series for the U.S. we are unable to reject the hypothesis that these series are non-stationary stochastic processes with no tendency to return to a trend line. Based on these findings and an unobserved components model for output that decomposes fluctuations into a secular or growth component and a cyclical component we infer that shocks to the former, which we associate with real disturbances, contribute substantially to the variation in observed output. We conclude that macroeconomic models that focus on monetary disturbances as a source of purely transitory fluctuations may never be successful in explaining a large fraction of output variation and that stochastic variation due to real factors is an essential element of any model of macroeconomic fluctuations.
In this note a functional central limit theorem for ϱ-mixing sequences of I. A. Ibragimov (Theory Probab. Appl.20 (1975), 135–141) is generalized to nonstationary sequences (Xn)n ∈ , satisfying some assumptions on the variances and the moment condition for some b > 0, ϵ > 0.
Power functions of tests of the random walk hypothesis versus stationary first-order autoregressive alternatives are tabulated for samples of fixed span but various frequencies of observation.
Let be a sequence of r.v.'s with . We prove the functional c.l.t. for under assumptions on and the asymptotic behaviour of for some . For the special cases of strongly mixing sequences with for some , or for some , we obtain functions such that for some is sufficient for the functional c.l.t., but the c.l.t. may fail to hold if .
The limit distribution of the least squares estimator of the parameter of the first order stochastic difference equation, in the boundary case , is calculated.
UnM cat. no.: 7701022. Thesis (Ph. D.)--Iowa State University, 1976. Includes bibliographical references (leaves 123-125). Microfilm. s
This Paper Studies Tests of Joint Hypotheses in Time Series Regression with a Unit Root in Which Weakly Dependent and Heterogeneously Distributed Innovations Are Allowed. We Consider Two Types of Regression: One with a Constant and Lagged Dependent Variable, and the Other with a Trend Added. the Statistics Studied Are the Regression \"F-Test\" Originally Analysed by Dickey and Fuller (1981) in a Less General Framework. the Limiting Distributions Are Found Using Functinal Central Limit Theory. New Test Statistics Are Proposed Which Require Only Already Tabulated Critical Values But Which Are Valid in a Quite General Framework (Including Finite Order Arma Models Generated by Gaussian Errors). This Study Extends the Results on Single Coefficients Derived in Phillips (1986A) and Phillips and Perron (1986).
Application of some advances in econometrics (in the theory of cointegrated vector autoregressive models) enables us to deal effectively with two problems in rational-expectations, present-valu e models: nonstationarity of time series and incomplete data on infor mation of market participants. With U.S. data, the authors find some relatively encouraging new results for the rational-expectations theo ry of the term structure and some puzzling results for the present-va lue model of stock prices. Copyright 1987 by University of Chicago Press.
Optimization of the part of consumers is shown to imply that the marginal utility of consumption evolves according to a random walk with trend. To a reasonable approximation, consumption itself should evolve in the same way. In particular, no variable apart from current consumption should be of any value in predicting future consumption. This implication is tested with time-series data for the postwar United States. It is confirmed for real disposable income, which has no predictive power for consumption, but rejected for an index of stock prices. The paper concludes that the evidence supports a modified version of the life cycle-permanent income hypothesis.
Even the best investors seem to find it hard to do better than the comprehensive common-stock averages, or better on the average than random selection among stocks of comparable variability. Examination of historical samples of percentage changes in a stock's price show that, when these relative price changes are properly adjusted for expected dividends paid out, they are more or less indistinguishable from white noise, or, at the least, their expected percentage movements constitute a driftless random walk (or random walk with mean drift specifiable in terms of an interest factor appropriate to the stock's variability or riskiness). The present contribution shows that such observable patterns can be deduced rigorously from a model which hypothesizes that a stock's present price is set at the expected discounted value of its future dividends, where the future dividends are supposed to be random variables generated according to any general (but known) stochastic process. This fundamental theorem follows by an easy superposition applied to the 1965 Samuelson theorem that properly anticipated futures prices fluctuate randomly -- i.e., constitute a martingale sequence, or a generalized martingale with specifiable mean drift. Examples demonstrate that even when the economy is not free to wander randomly, intelligent speculation is able to whiten the spectrum of observed stock-price changes. A subset of investors might have better information or modes of analysis and get above average gains in the random-walk model; and the model's underlying probabilities could be shaped by fundamentalists' economic forces.
I study the dynamics of oil futures prices in the NYMEX using a large panel dataset that includes global macroeconomic indicators, financial market indices, quantities and prices of energy products. I extract common factors from the panel data series and estimate a Factor-Augmented Vector Autoregression for the maturity structure of oil futures prices. I find that latent factors generate information that, once combined with that of the yields, improves the forecasting performance for oil prices. Furthermore, I show that a factor correlated to purely financial developments contributes to the model performance, in addition to factors related to energy quantities and prices.
This paper describes a simple method of calculating a heteroskedasticity and autocorrelation consistent covariance matrix that is positive semi-definite by construction. It also establishes consistency of the estimated covariance matrix under fairly general conditions.
The concept of a near-integrated vector random process is introduce d, helping the author work towards a general asymptotic theory of regression fo r multiple time series in which some series may be integrated processe s of the ARIMA type, others may be stable ARMA processes with near unit roots, and yet others may be mildly explosive. A limit theory for th e sample moments of such time series is developed using weak convergence. The theory is applied to the study of vector autoregress ions and cointegrating regressions of the type advanced by R. F. Engle and C. W. Granger (1987). A noncentral limiting distribution theory is derived for some recently-proposed multivariate unit root tests. Models with drift and near-integration are also studied. Copyright 1988 by The Econometric Society.
This paper studies how financial markets in the US and Mainland China affected equity, money and foreign exchange markets in Hong Kong on daily basis during the current financial crisis, and how these financial linkages have changed compared with the experience in 2001. In the equity markets, the influence of the Mainland on Hong Kong has increased substantially in the current financial crisis, but it is still less important than that of the US. In the money market, correlation between HIBOR and LIBOR has picked up from the low levels observed during the tranquil period before the crisis, to almost the same level of correlation as observed during the IT bubble burst. In the foreign exchange market, the daily movements of the Hong Kong dollar/US dollar exchange rate have been rather small and mainly influenced by the short-term interest rates. Fund flows in different directions might have neutralised the impact of other markets on the foreign exchange market. A broad interpretation of these findings is that Hong Kong financial markets appear to be more aligned with the US markets in turbulent times, but relatively more integrated with the Mainland markets during the tranquil periods.
This paper provides general conditions which ensure consistency and asymptotic normality for the nonlinear least squares estimator. These conditions apply to time-series, cross-section, panel, or experimental data for single equations as well as systems of equations. The regression errors may be serially correlated and/or heteroscedastic. For an important special case, we propose a new covariance matrix estimator which is consistent regardless of the presence of heteroscedasticity or serial correlation of unknown form. We also give some new tests for model misspecification, based on the information matrix testing principle.
This paper investigates the distribution of the least squares estimator of the coefficient α in the model @c"t = @a@c"t -"1 + @?"t where the @?"t where the @?"t are independently distributed N (O, @s^2). The exact finite sample and limiting distributions are calculated when α ≥ 1 and finite sample distributions when α
"Nowhere does history indulge in repetitions so often or so uniformly as in Wall Street," observed legendary speculator Jesse Livermore. History tells us that periods of major technological innovation are typically accompanied by speculative bubbles as economic agents overreact to genuine advancements in productivity. Excessive run-ups in asset prices can have important consequences for the economy as firms and investors respond to the price signals, resulting in capital misallocation. On the one hand, speculation can magnify the volatility of economic and financial variables, thus harming the welfare of those who are averse to uncertainty and fluctuations. But on the other hand, speculation can increase investment in risky ventures, thus yielding benefits to a society that suffers from an underinvestment problem.
Tests are conducted for the presence of unit roots in the autoregressive representations of the logarithms of spot and forward exchange rates. The results from these tests provide one explanation for some of the conflicting conclusions which emerge from recent empirical papers on the foreign exchange market.
My initial motivation for considering volatility measures in the efficient markets models was to clarify the basic smoothing properties of the models to allow an understanding of the assumptions which are implicit in the notion of market efficiency. The efficient markets models, which are described in section II below ,relate a price today to the expected present value of a path of future variables. Since present values are long weighted moving averages, it would seem that price data should be very stable and smooth. These impressions can be formalized in terms of inequalities describing certain variances (section III). The results ought to be of interest whether or not the data satisfy these inequalities, and the procedures ought not to be regarded as just "another test" of market efficiency. Our confidence of our understanding of empirical phenomena is enhanced when we learn how such an obvious property of data as its "smoothness" relates to the model, and to alternative models (section IV below).On further examination of the volatility inequalities, it became clear that the inequalities may also suggest formal tests of market efficiency that have distinct advantages over conventional tests. These advantages take the form of greater power in certain circumstances of robustness to data errors such as misalignment and of simplicity and understandability. An interpretation of volatility tests versus regression tests in terms of the likelihood principle is offered in section V.
Tests for unit roots: A Monte Carlo investigation, Mimeo. (Graduate School of Business Administration
- G W Schwert
Schwert, G.W., 1987, Tests for unit roots: A Monte Carlo investigation, Mimeo. (Graduate School of Business Administration, University of Rochester, Rochester, NY).
Capital in the American economy
- S Kuznets
Kuznets, S., 1961, Capital in the American economy (National Bureau of Economic Research, Cambridge).