Non-stationarity Tests Research Articles

Market efficiency of the top market-cap cryptocurrencies: Further evidence from a panel framework

This paper re-visits the Efficient Market Hypothesis for 31 of the top market-cap cryptocurrencies using various panel tests. We first examine cross-sectional dependence in panels for these cryptocurrencies to inform the subsequent use of tests for non-stationarity. Next, we utilise panel unit root/stationarity tests that allow for any cross-sectional dependence and takes into account possible structural breaks in the panels to jointly examine the efficiency of cryptocurrencies. The panel evidence suggests no empirical support for the hypothesis, indicating market inefficiency in cryptocurrencies.

Revisiting the environmental Kuznets curve (EKC) hypothesis in India: the effects of energy consumption and democracy.

The study revisits the position of the environmental Kuznets curve (EKC) hypothesis in India by incorporating the role of energy consumption and democratic regime in the environmental degradation function for the period 1971-2014. Employing Zivot-Andrews nonstationarity test, Bayer-Hanck cointegration test, autoregressive distributed lag (ARDL) model, and vector autoregressive model (VECM) Granger causality test, the results found the integration order of I(1) and a stable cointegration among the series. The result validates the EKC hypothesis for India and further divulges that while energy consumption increases environmental degradation both in the long run and short run; the effect of democracy in reducing environmental degradation is weak (statistically insignificant) in the long run but strong (statistically significant) in the short run. The finding from the VECM Granger causality test indicates a long-run causality between the fundamental variables and environmental degradation. Furthermore, the results of the short run show a unidirectional Granger causality running from energy consumption to environmental degradation, energy consumption to real income, and energy consumption to square of real income. Therefore, our findings suggest that energy conservation policy should be prioritized towards harnessing energy from clean sources to mitigate environmental degradation and spur economic growth.

Assessing the Impacts of Correlated Variability with Dissociated Timescales.

Despite the profound influence on coding capacity of sensory neurons, the measurements of noise correlations have been inconsistent. This is, possibly, because nonstationarity, i.e., drifting baselines, engendered the spurious long-term correlations even if no actual short-term correlation existed. Although attempts to separate them have been made previously, they were ad hoc for specific cases or computationally too demanding. Here we proposed an information-geometric method to unbiasedly estimate pure short-term noise correlations irrespective of the background brain activities without demanding computational resources. First, the benchmark simulations demonstrated that the proposed estimator is more accurate and computationally efficient than the conventional correlograms and the residual correlations with Kalman filters or moving averages of length three or more, while the best moving average of length two coincided with the propose method regarding correlation estimates. Next, we analyzed the cat V1 neural responses to demonstrate that the statistical test accompanying the proposed method combined with the existing nonstationarity test enabled us to dissociate short-term and long-term noise correlations. When we excluded the spurious noise correlations of purely long-term nature, only a small fraction of neuron pairs showed significant short-term correlations, possibly reconciling the previous inconsistent observations on existence of significant noise correlations. The decoding accuracy was slightly improved by the short-term correlations. Although the long-term correlations deteriorated the generalizability, the generalizability was recovered by the decoder with trend removal, suggesting that brains could overcome nonstationarity. Thus, the proposed method enables us to elucidate the impacts of short-term and long-term noise correlations in a dissociated manner.

Improving the Performance of a Long‐Run Variance Ratio Test for a Unit Root

Cai and Shintani (2006, Econometric Theory, 22, 347–372) considered the impact of introducing an inconsistent long-run variance estimator when constructing a class of kernel-based ratio tests for testing non-stationarity in the series. They found that the quotient of two estimators with different rates of convergence under the null and the alternative hypotheses may lead to a test having an interesting size and power trade-off. This paper develops modified versions of this test, presents new asymptotic results and tabulates critical values. The finite sample performance is explored through Monte Carlo simulations. The results show that the modifications proposed lead to more powerful unit root tests.

The INR/USD Exchange Rate Determination: An Empirical Investigation of the Flexible Price Monetary Model in a Vector Auto Regression Framework

The current study attempts to examine the importance of the Flexible Price Monetary (FPM) Model in explaining the INR/USD exchange rate movement with macro variables such as relative money stock, relative rates of interest and relative output for the period from April 1995 till December 2016. Prior to estimating the empirical model, an array of non-stationarity tests was employed to identify the time series characteristics of the data. Since all the data series were confirmed to be integrated of order one, the multivariate cointegration methodology was used to verify long-run validity of the model. The empirical results garner support for the FPM model in determining INR/USD exchange rate in the long run. The test on direction of causality confirmed existence of causality from FPM variables to exchange rate. The empirical model was estimated in the Vector Auto regression (VAR) framework and variance decomposition analysis was used to examine fluctuation in INR/USD exchange rate caused by the shocks in FPM model variables. It was found that, the monetary model variables explain the exchange rate patterns over a longer period of time but was found not very effective in the short run and hence cannot be considered as a useful framework in explaining the variations in INR/USD exchange rate.

Performance Evaluation of four Statistical Tests for Trend and Non-stationarity and Assessment of Observed and Projected Annual Maximum Precipitation Series in Major United States Cities

In this study, the performance of four statistical tests was evaluated to assess the following time-series types: stationary in variance and trend in mean (S_T), stationary in variance and no trend in mean (S_NT), nonstationary in variance and trend in mean (NS_T), and nonstationary in variance and no trend in mean (NS_NT). The four statistical tests included two stationarity tests, the Kwiatkowski–Phillips–Schmidt–Shin (KPSS) and Philips and Perron (PP) tests, and two trend tests, the Mann-Kendall (M-K) and regression tests. In each case, the sample size, standard deviation for noise, and several parameters were randomly generated to produce 1000 samples. The four tests were then conducted to determine if the data were stationary or non-stationary with trend or without trend. The results showed that there are several important patterns depending on the conditions of Monte Carlo experiments to investigate the performances of the four statistical tests with the four time-series types. These tests were also conducted to evaluate the time-series types of the observed and projected annual daily maximum precipitation series in eight cities of the United States. Results showed that cases of S_NT, which is the general assumption for the classical statistical frequency analysis, became less represented, while the two trend cases (NS_T and S_T) became more represented as time went on from HIST (1950–1999) to a representative concentration pathway (RCP) 4.5 or RCP 8.5 (2000–2099). NS_T cases in RCP 8.5 occurred more frequently than those in RCP 4.5. These results suggest that because of climate change, the assessment of time-series types should be considered when examining annual maximum precipitation and designing water-related infrastructure.

MIXED GEOGRAPHICALLY WEIGHTED REGRESSION USING ADAPTIVE BANDWIDTH TO MODELING OF AIR POLLUTER STANDARD INDEX

Air pollution is one of the most concerned problems on earth today. It is closely related with and mostly generated from the transportation and industrialization sectors, as well as from the environmentally degrading effect of the urban physical development. Air pollution promotes the lower level of air quality, which in turn promotes the greater risk on health, especially that of the human being. This research aims to aid the government in the policy making process related to air pollution mitigation by developing a standard index model for air polluter (Air Polluter Standard Index - APSI) based on the Mixed Geographically Weighted Regression (MGWR) approach using the adaptive bandwidth. The adaptive bandwidth kernel has different bandwidth value in each observation location. Akaike Information Criterion-corrected (AICc) value is used to choose the most optimum bandwidth. The Monte Carlo Simulation is used to tests for regression coefficient non-stationarity. In this research, we also consider seven variables that are directly related to the air pollution level, which are the traffic velocity, the population density, the business center aspect, the air humidity, the wind velocity, the air temperature, and the area size of the urban forest. Based on AICc and MSE value it is know that the MGWR model with adaptive bisquare kernel is the best bandwidth to analyze this model.

Effects of atmospheric nonstationarity on models of low-frequency surface wind noise

Measurements of sound propagation in the atmosphere are often limited by wind noise, particularly at low frequencies. The spectrum of wind noise at the ground surface, i.e. turbulent static pressure, can be modeled by the dominant shear-turbulence mechanism within the atmospheric boundary layer. This model assumes statistically-stationary boundary-layer turbulence, and as in the atmospheric sciences, quasi-stationarity is hypothesized to justify the assumption. However, this hypothesis is not uniformly valid, due to the diurnal cycle and large-scale atmospheric dynamics, and should be tested. This study applies several existing tests of nonstationarity to atmospheric measurements from a field experiment near Laramie, Wyoming and characterizes their relevance to simultaneous recordings of wind noise by flush-mounted infrasound sensors. By estimating the parameters for a mirror flow model of boundary-layer turbulence from the anemometer records, surface pressure model spectra are compared with the experimental wind noise. The performance of both the atmospheric turbulence and wind noise models are assessed with respect to each nonstationarity test.

Climate change effects and extreme rainfall non-stationarity

It is necessary to perform analysis to confirm stationarity or detect non-stationarity of extreme rainfall data in order to derive accurate design rainfall estimates for hydraulic structure design. In this study, non-stationarity of extreme rainfalls in the Antalya region in Turkey was investigated through statistical non-stationarity tests and stationary and non-stationary generalised extreme value distribution models. After determination of stationarity of extreme rainfalls in the Antalya region, a frequency analysis was conducted in a stationary context to derive design rainfall intensities. Future (2080–2099) design rainfall intensities were then estimated and bias corrected, and current and future design rainfall intensities were compared and discussed. Non-stationarity analysis showed no evidence of non-stationarity in Antalya. Bias-corrected future design rainfall intensity estimates showed that design rainfall intensities in the future are expected to be larger than current design rainfall intensities for return periods of 5, 10, 20, 50 and 100 years. This study is expected to contribute to a better understanding of the relationship between global warming and extreme rainfall in one of the most climate change sensitive parts of Turkey.

Small area prediction of counts under a non-stationary spatial model

There is a growing need for current and reliable counts at small area level. The empirical predictor under a generalised linear mixed model (GLMM) is often used for small area estimation (SAE) of such counts. However, the fixed effect parameters of a GLMM are spatially invariant and do not account for the presence of spatial nonstationarity in the population of interest. A geographically weighted regression extension of the GLMM is developed, extending this model to allow for spatial nonstationarity, and SAE based on this spatially nonstationary model (NSGLMM) is described. The empirical predictor for small area counts (NSEP) under an area level NSGLMM is proposed. Analytic and bootstrap approaches to estimating the mean squared error of the NSEP are also developed, and a parametric approach to testing for spatial nonstationarity is described. The approach is illustrated by applying it to a study of poverty mapping using socio-economic survey data from India.

Do global CO2 emissions from fossil-fuel consumption exhibit long memory? a fractional-integration analysis

ABSTRACTIn this article we use an autoregressive fractionally integrated moving average approach to measure the degree of fractional integration of aggregate world CO2 emissions and its five components – coal, oil, gas, cement, and gas flaring. We find that all variables are stationary and mean reverting, but exhibit long-term memory. Our results suggest that both coal and oil combustion emissions have the weakest degree of long-range dependence, while emissions from gas and gas flaring have the strongest. With evidence of long memory, we conclude that transitory policy shocks are likely to have long-lasting effects, but not permanent effects. Accordingly, permanent effects on CO2 emissions require a more permanent policy stance. In this context, if one were to rely only on testing for stationarity and non-stationarity, one would likely conclude in favour of non-stationarity, and therefore that even transitory policy shocks have permanent effects. Our fractional-integration analysis highlights that this is not the case.

New evidence on breaking trend functions in real GDPs from Great China Economic Area

ABSTRACTThis article explores the difference in the time series property of economic output for the Great China Economic Area (GCEA) (Mainland China, Hong Kong and Taiwan). Using the powerful Kim and Perron (2009) unit root test and real GDPs over the period 1992–2014 as the study sample, results indicate the presence of a break for all economies that corresponds to the Asian financial crisis. Additionally, allowing for a break leads to the rejection of the unit root hypothesis for Taiwan only. Important implications are provided. First, considering the presence of a break in testing for nonstationarity is important or false conclusions can be drawn. Second, given the stationarity of GDP found for Taiwan only, investors should look beyond any local economic shocks and focus more on world economy development when investing in Taiwan. By contrast, investors in Mainland China and Hong Kong should pay attention to any shock because it is likely to be persistent. Third, relevant authorities should recognize that any government policy intended to promote long-run economic growth may be ineffective in Taiwan whereas it can be more effective in Mainland China and Hong Kong.

A simple test for nonstationarity in mixed panels: A further investigation

The test of Ng (2008) is one of the few that enables general inference regarding the proportion of non-stationary units in panel data. The current paper furthers the investigation of Ng (2008) in two directions. First, the existing sequential limit analysis is generalized to a very flexible asymptotic framework in which the number of time periods, T, can be either fixed or tending to infinity jointly with the number of cross-section units, N. Second, the test statistic is evaluated not only under the null hypothesis, but also under alternatives that can be either fixed or local.

Local non-stationarity test in mean for Markov switching GARCH models: an approximate Bayesian approach

In order to exploit mean-reverting behavior among the price differential between two markets, one can use unit root tests to determine which pairs of assets appear to exhibit mean-reverting behavior. Since nonlinear mean reversion shares the same meaning as local stationarity, this paper proposes a Bayesian hypothesis testing to detect the presence of a local unit root in the mean equation using Markov switching GARCH models. This model incorporates a fat-tailed error distribution to analyze asymmetric effects on both the conditional mean and conditional volatility of financial time series. To implement the test, we propose a numerical approximation of the marginal likelihoods to posterior odds by using an adaptive Markov Chain Monte Carlo scheme. Our simulation study demonstrates that the approximate Bayesian test performs properly. The proposed method utilizes the daily basis between the FTSE 100 Index and Index Futures as an illustration.

Testing for the Stationarity in Total Factor Productivity: Nonlinearity Evidence from 79 Countries

Several studies have conducted empirical research on different aspects of total factor productivity. However, the estimation of its degree of integration, which has important usefulness for policy formulation, forecasting purposes and econometric modeling, has been greatly overlooked in the literature. The purpose of this paper is to examine the stationarity properties of total factor productivity in 79 economies for the period 1970–2011. Using a newly constructed dataset and a new nonstationarity test that provide for nonlinearity in the estimations, the empirical results show that the series in 67 countries (or 85 % of the total sample) follow the unit root process. In other words, the total factor productivity in these countries are integrated of order one. For the remaining 12 countries (or 15 % of the total sample), we observe that the series exhibit stationary process. We discuss the policy implications of these findings and offer suggestions for further research.

Brazil-US trade balance and exchange rate: Dynamic empirics

Brazil and USA are important trading partners. Brazil as a resource-rich country in Latin America and a vibrant emerging economy draws enormous US trade and investment interests. Inclusion in BRICS lifts Brazil as an emerging global economic force and BRICS as a group poses economic challenges to the developed world. The Brazil-US growing trade and fluctuating Real-Dollar exchange rate are a fascinating issue of empirical exploration. The principal objective of this paper is to study the dynamics between Brazil-US nominal trade balance and nominal Real-Dollar exchange rate. Monthly data are utilized from January 1999 through December 2013 since Brazil allowed floatation of Real beginning in January 1999. They are obtained from the Direction of Trade and International Financial Statistics, published by the IMF. The standard cointegration methodology is implemented. This is appropriate since macroeconomic and financial variables are very likely to be time-variant. The application of OLS on nonstationary variables would produce misleading inferences in presence of spurious correlation. Consequently, the efficient DF-GLS and NG-Perron tests for nonstationarity and their counterpart KPSS test for stationarity are applied. All of them confirm nonstationarity of both time series variables. Stationarity in both variables is restored on first-differencing of the level data depicting I(1) behavior. Consequently, the Johansen-Juselius procedure is implemented for cointegrating relationship. Both λ max and λ trace test statistics unveil no cointegration between nominal bilateral trade balance and exchange rate. In this backdrop, VAR model is estimated, as appropriate. The evidences on short-run bidirectional causal flows are strong with significant interactive feedback effects. In the case of reverse causality, the evidences are highly insignificant. The impulse response analysis depicts the existence of short-run bilateral J-curve that shows initial deterioration in trade balance for a while following exchange rate depreciation before improvement into positive territory. In this paper, the J-curve shows that currency depreciation by Brazil against the US dollar to improve its trade balance with the USA may work only in the short run. Progressive improvement in trade balance in the long run would, in fact, depend on prudent monetary and fiscal actions to enhance Brazil’s global competitiveness through improvement in labor productivity and modern technology adoption.

Purchasing Power Parity: A Unit Root, Cointegration and VAR Analysis in Emerging and Advanced Countries

The purpose of this study is to investigate the validity of the absolute version of the purchasing power parity (PPP) of a sample of four advanced and four emerging countries covering the period from 1993 to 2014. To examine the existence of PPP we apply the Augmented Dickey-Fuller, DF-GLS and KPSS tests for non-stationarity, and the Johansen procedure for cointegration between exchange rates and consumer price indices. The impulse response function presents a graphical view which is consistent with impressions from the statistics of stationarity tests. We also employ the variance decomposition method to analyze the movements in the exchange rates and the price indices that are caused by their own shocks, and shocks caused by other variables. With respect to half-life estimates, the results from a shock to the real exchange rate range from 0.81 to 6.45 years (3.23 years on average). Overall, unit root tests show that absolute PPP may not hold, but this depends on the country and the selected method. In contrast, the Johansen approach does not support the existence of PPP for both developed countries and emerging market economies.

Using Bootstrap Methods to Investigate Coefficient Non-stationarity in Regression Models: An Empirical Case Study

In this study, parametric bootstrap methods are used to test for spatial non-stationarity in the coefficients of regression models (i.e. test for relationship non-stationarity). Such a test can be rather simply conducted by comparing a model such as geographically weighted regression (GWR) as an alternative to a standard regression, the null hypothesis. However here, three spatially autocorrelated regressions are also used as null hypotheses: (i) a simultaneous autoregressive error model; (ii) a moving average error model; and (iii) a simultaneous autoregressive lag model. This expansion of null hypotheses, allows an investigation as to whether the spatial variation in the coefficients obtained using GWR could be attributed to some other spatial process, rather than one depicting non-stationary relationships. In this short presentation, the bootstrap approach is applied empirically to an educational attainment data set for Georgia, USA. Results suggest value in the bootstrap approach, providing a more informative test than any related test that is commonly applied.

Purchasing Power Parity: Evidence from Selected High and Low Inflation Countries

This paper reexamines the long run relationship between nominal bilateral exchange rate and the price index ratio for high and low inflation countries using time series analysis techniques. Tests for non-stationarity were carried out before cointegration analysis was conducted. Theoretically, Purchasing Power Parity (PPP) should receive empirical support in the case of high-inflation countries. This is because PPP is a monetary phenomenon and monetary factors tend to overshadow real factors in high-inflation countries. The findings show that high inflation countries such as Sierra Leone and Mexico support the Theory of Purchasing Power Parity (PPP). In the case of low inflation countries, none of the countries provides evidence supporting theory of PPP.

Purchasing Power Parity: A Unit Root, Cointegration and VAR Analysis in Emerging and Advanced Countries

The purpose of this study is to investigate the validity of the absolute version of the purchasing power parity (PPP) of a sample of four advanced and four emerging countries covering the period from 1993 to 2014. To examine the existence of PPP we apply the Augmented Dickey-Fuller, DF-GLS and KPSS tests for non-stationarity, and the Johansen procedure for cointegration between exchange rates and consumer price indices. The impulse response function presents a graphical view which is consistent with impressions from the statistics of stationarity tests. We also employ the variance decomposition method to analyze the movements in the exchange rates and the price indices that are caused by their own shocks, and shocks caused by other variables. With respect to half-life estimates, the results from a shock to the real exchange rate range from 9,76 to 77,39 months. Overall, unit root tests show that absolute PPP may hold, but this depends on the country and the selected method. In contrast, the Johansen approach does not support the existence of PPP in any country.