Null Hypothesis Of Unit Root Research Articles

Unit Root Tests for Dependent Micropanels

This paper proposes a new test for the null hypothesis of panel unit roots for micropanels with short time dimensions (T) and large cross-sections (N). There are several distinctive features of this test. First, the test is based on a panel AR(1) model allowing for cross-sectional dependency, which is introduced by a factor structure of the initial condition. Second, the test employs the panel AR(1) model with AR(1) coefficients that are heterogeneous for finite N. Third, the test can be used both for the alternative hypothesis of stationarity and for that of explosive roots. Fourth, the test does not use the AR(1) coefficient estimator. The effectiveness of the test rests on the fact that the initial condition has permanent effects on the trajectory of a time series in the presence of a unit root. To measure the effects of the initial condition, the present paper employs cross-sectional regressions using the first time-series observations as a regressor and the last as a dependent variable. If there is a unit root in every individual time series, the coefficient of the regressor is equal to one. The t-ratios for the coefficient are this paper’s test statistics and have a standard normal distribution in the limit. The t-ratios are based on the OLS estimator and the instrumental variables estimator that uses reshuffled regressors as instruments. The test proposed in this paper makes it possible to test for a unit root even at T = 2 as long as N is large. Simulation results show that test statistics have reasonable empirical size and power. The test is applied to college graduates’ monthly real wage in South Korea. The number of time-series observations for this data is only two. The null hypothesis of a unit root is rejected against the alternative of stationarity.

Structural breaks and unit root in macroeconomic time series: evidence from Nigeria

The discourse on the properties of macroeconomic time series has received a considerable interest in recent literature. This is because the presence of unit in a realization of a stochastic process implies that shocks to the time series have a persistent effect with policy implications. Hence, this paper investigates the unit root properties of ten Nigerian macroeconomic time series using quarterly data from 1981-2015. For comparison, first we apply the conventional augmented Dickey-Fuller unit root test to examine the null of a unit root in the ten macroeconomic series, and we proceed to examine the unit root properties using the Lagrange Multiplier (LM) endogenous unit root tests that account for the presence of one-break and two-break as proposed by Lee and Strazicich (2003, 2013). On employing the augmented Dickey-Fuller test that does not account for structural breaks, our empirical results indicate that the unit root null hypothesis cannot be rejected for nine of the ten series considered in the study. However, on utilizing the Lagrange Multiplier (LM) endogenous one and two structural breaks test, we reject the unit root null in favour of the one and two-break stationary alternative for six of the ten series (60% rejection) considered in our study. These results imply that unit root tests that do not account sufficiently for the presence of structural breaks lead to misleading inference. These findings have important implications for the macroeconomic policy-making, modeling and forecasting of the Nigerian economy. We therefore, recommend that structural breaks should be taken into account in the econometric analysis of Nigerian macroeconomic variables.

On the Use of GLS Demeaning in Panel Unit Root Testing

One of the most well-known facts about unit root testing in time series is that the Dickey–Fuller (DF) test based on ordinary least squares (OLS) demeaned data suffers from low power, and that the use of generalized least squares (GLS) demeaning can lead to substantial power gains. Of course, this development has not gone unnoticed in the panel unit root literature. However, while the potential of using GLS demeaning is widely recognized, oddly enough, there are still no theoretical results available to facilitate a formal analysis of such demeaning in the panel data context. The present article can be seen as a reaction to this. The purpose is to evaluate the effect of GLS demeaning when used in conjuncture with the pooled OLS t-test for a unit root, resulting in a panel analog of the time series DF–GLS test. A key finding is that the success of GLS depend critically on the order in which the dependent variable is demeaned and first-differenced. If the variable is demeaned prior to taking first-differences, power is maximized by using GLS demeaning, whereas if the differencing is done first, then OLS demeaning is preferred. Furthermore, even if the former demeaning approach is used, such that GLS is preferred, the asymptotic distribution of the resulting test is independent of the tuning parameters that characterize the local alternative under which the demeaning performed. Hence, the demeaning can just as well be performed under the unit root null hypothesis. In this sense, GLS demeaning under the local alternative is redundant.

Foreign tourist arrivals in India from major source countries: an empirical analysis

The tourism industry is a significant contributor to the world economy and needs to be carefully evaluated for impact by influencing factors such as external shocks. Several practical implications are associated with the testing of the unit root hypothesis in the context of foreign tourist arrivals in India. For instance, if the unit root process is followed, it implies that shocks to foreign tourist arrivals are permanent in nature rather than temporary. This study employed a battery of time series unit root tests in an attempt to examine whether foreign tourist arrivals in India from 17 major source countries between 1981 and 2012 were permanently or temporarily affected by shocks. The empirical results of this study revealed that shocks to foreign tourist arrivals in India from eight source countries have only a temporary effect and shocks form rest of nine countries have permanent impact. It may therefore be concluded that the government should focus on long-term solutions for those eight source countries where the null hypothesis of unit root is rejected in order to promote international tourist arrivals rather than implementing temporary measures.

Is per capita energy use stationary? Time series evidence for the EMU countries

This study examines the stationary properties of per capita energy use in the 19 Eurozone member countries by using annual data over 1960–2013 period. We utilize the Clemente et al. unit root test that determines structural breaks. Empirical results show that most of the country series does not reject the unit root null hypothesis at the 5% significance level, both in the case of additive outlier and of innovative outlier. Therefore, our empirical findings provide significant evidence that energy use is nonstationary in almost all Eurozone countries. For the policy makers, it is necessary to pay attention to energy use series.

A time series paradox: Unit root tests perform poorly when data are cointegrated

Cointegration among times series paradoxically makes it more likely that a unit test will reject the unit root null hypothesis on the individual series. This occurs because at least one series in the system has a negative moving average component.

Is per capita energy use stationary? Time series evidence for the EMU countries

This study examines the stationary properties of per capita energy use in the 19 Eurozone member countries by using annual data over 1960–2013 period. We utilize the Clemente et al. unit root test that determines structural breaks. Empirical results show that most of the country series does not reject the unit root null hypothesis at the 5% significance level, both in the case of additive outlier and of innovative outlier. Therefore, our empirical findings provide significant evidence that energy use is nonstationary in almost all Eurozone countries. For the policy makers, it is necessary to pay attention to energy use series.

Quantile unit root test and the PPP in Africa

ABSTRACTIn this study, we apply the Quantile unit root test and revisit the Purchasing Power Parity (PPP) in 20 African countries using real effective exchange rates over the period 1971Q1 to 2012Q4. While traditional unit root tests fail to reject unit root hypothesis in most of the countries, results from Quantile unit root test reject unit root null hypothesis in Ghana, Mauritius, Niger, South Africa, and Togo, providing support for the PPP at least in these five countries. We further estimate the half-life based on Quantile autoregressive (QAR) model to be about 4.57–7.96 quarters (1–2 year).

Do rice prices follow a random walk? Evidence from Markov switching unit root tests for Asian markets

This study revisits the issue of mean reversion in the import rice prices of six Asian countries over the period between 1995 and 2015. Augmented Dickey Fuller tests with a conventional linear regression model support the presence of a unit root in the levels of the price data. However, when regressions allow for Markov switching in coefficients and variances to capture periodic shifts in levels and volatilities, there is strong evidence against the unit-root null hypothesis in favor of stationarity over much of the observation period.

Revisiting purchasing power parity in Eastern European countries: quantile unit root tests

This study applies quantile unit root test proposed by Koenker and Xiao (J Am Stat Assoc 99(467):775–787, 2004) and Galvao (J Econom 152:165–178, 2009) to revisit the purchasing power parity in 7 transition countries: Bulgaria, Czech Republic, Hungary, Lithuania, Poland, Romania, and Russia over 1998M1 to 2015M3. While traditional unit root tests fail to reject unit root hypothesis, the two quantile unit root tests did reject unit root null hypothesis in all countries, providing support for the PPP and solving the PPP puzzle. The estimated half-life based on quantile autoregressive model is about 12–25 months (1–2 year).

Persistence, mean reversion and non-linearities in the US housing prices over 1830–2013

ABSTRACTThe objective of this study is to provide a direct estimate of the degree of persistence of measures of nominal and real house prices for the US economy, covering the longest possible annual sample of data, namely 1830–2013. The estimation of the degree of persistence accommodates for non-linear (deterministic) trends using Chebyshev polynomials in time. In general, the results show a high degree of persistence in the series along with a component of non-linear behaviour. In general, if we assume uncorrelated errors, non-linearities are observed in both nominal and real prices, but this hypothesis is rejected in favour of linear models for the log-transformation of the data. However, if autocorrelated errors are permitted, non-linearities are observed in all cases, and mean reversion is found in the case of logged prices, though given the wide confidence intervals, the unit root null hypothesis cannot be rejected in these cases.

Exchange rate persistence of the Chinese yuan against the US dollar in the NDF market

This article analyses the persistence of the exchange rates of the Chinese yuan against the US dollar in the NDF market during 1999–2012 with fractional integration technique. It concludes that the exchange rates are I(d) with d close to 1 though statistically significantly below 1, suggesting a small degree of mean reverting behaviour. And the squared returns display long memory with an order of integration of about 0.2. Moreover, the unit root null hypothesis cannot be rejected during the years during 2006–2011 when the international financial crisis broke out and the exchange rate regime reform implemented. At last, we notice that d in the original series is highly negatively correlated with respect to the mean and the variance in the exchange rates, while it is positively correlated with them in the squared returns. And policy implications are also suggested.

A GARCH model for testing market efficiency

In this paper we propose a generalised autoregressive conditional heteroskedasticity (GARCH) model-based test for a unit root. The model allows for two endogenous structural breaks. We test for unit roots in 156 US stocks listed on the NYSE over the period 1980 to 2007. We find that the unit root null hypothesis is rejected in 40% of the stocks, and only in four out of the nine sectors the null is rejected for over 50% of stocks. We conclude with an economic significance analysis, showing that mostly stocks with mean reverting prices tend to outperform stocks with non-stationary prices.

Fixed and Recursive Right-Tailed Dickey–Fuller Tests in the Presence of a Break under the Null

AbstractRight-tailed Dickey–Fuller-type unit root tests against the explosive alternative have become popular in economics and finance for detecting asset price bubbles. This paper studies the size properties of fixed sample and recursive right-tailed Dickey–Fuller tests if the relevant series contains a unit root, but a structural break in the drift parameter occurs. It is shown that positive size distortion and therefore spurious rejections of the unit root null hypothesis in favour of the explosive alternative can be a problem for both types of test. Some possible solutions to this problem are briefly discussed.

Breaks, trends, and unit roots in spot prices for crude oil and petroleum products

This study examines the trend properties in energy price series using weekly spot price data for crude oil, heating oil, and regular gasoline. In particular, the procedures proposed by Perron and Yabu (2009b) are employed to test for a one-time break in the trend function of each price series with no prior knowledge of whether the noise component is stationary or has an autoregressive unit root. Based on the results of the break estimate, the unit root test developed by Kim and Perron (2009) is performed to examine the stationarity of the prices. Finally, we extend the one-break analysis to the case with multiple breaks by employing the break test proposed by Kejriwal and Perron (2010) and the unit root test of Carrion-i-Silvestre et al. (2009). The results consistently demonstrate evidence of structural breaks and reject the unit root null hypothesis for all the price series, suggesting that energy prices are persistently influenced by long-term economic fundamentals instead of temporal policy changes.

Examining the Islamic stock market efficiency: Evidence from nonlinear ESTAR unit root tests

This paper empirically examines the efficient market hypothesis (EMH) in the Islamic stock market namely Jakarta Islamic Index by emphasizing on the random walk behavior and nonlinearity. In the first step, we employ Brock et al. (1996) test to examine the presence of nonlinear behavior in Jakarta Islamic Index. The evidence of nonlinear behavior in the indices, motivate us to use nonlinear ESTAR unit root test procedure recently developed by Kapetanios et al. (2003) and Kruse (2011). The nonlinear unit root test procedure fail to rejects the null hypothesis of unit root for the indices, suggesting that Jakarta Islamic Index characterized by random walk process supporting the theory of efficient market hypothesis. In addition, Lumsdaine and Papel (LP) test identified significant structural breaks in the index series.

Can the hysteresis hypothesis in Spanish regional unemployment be beaten? New evidence from unit root tests with breaks

This paper tests the hysteresis hypothesis in Spanish regional unemployment using quarterly data over the 1976–2014 period using a large battery of univariate unit root tests allowing for two breaks in the trend function of the series. The evidence strongly supports the hysteresis hypothesis for each of the 17 Spanish regions, since we consistently fail to reject the unit root null hypothesis. When the analysis is extended to allow for five structural breaks, the conclusion remains unaltered. The results call for policy measures to reduce the sluggishness in the adjustment of the labour market to adverse shocks.

Is the efficient market hypothesis day-of-the-week dependent? Evidence from the banking sector

In this article, we propose a new hypothesis: that the efficient market hypothesis is day-of-the-week-dependent. We apply the test to firms belonging to the banking sector and listed on the NYSE. We find significant evidence that the efficient market hypothesis is day-of-the-week-dependent. Overall, for only 62% of firms, the unit root null hypothesis is rejected on all the five trading days. We also discover that when investors do not account for unit root properties in devising trading strategies, they obtain spurious profits.

Time series behaviour of the real interest rates in transition economies

Stationarity properties of real interest rates are examined for 21 transition economies. Owing to transaction costs and other frictions, it is quite plausible that we are dealing with potential non-linearities in the real interest rate. Therefore we examine stationarity of the real interest rate allowing for non-linearities and asymmetric adjustment with smooth structural change in the data generating process. Our findings suggest that taking account of non-linearities in the data generating process results in a rejection of the unit root null hypothesis for some countries which seem to be non-stationary according to conventional unit root tests. This finding points to the importance of allowing for both structural breaks and asymmetric adjustment in the real interest rate series of transition countries.

A unit root model for trending time-series energy variables

In this paper, we propose a GARCH-based unit root test that is flexible enough to account for; (a) trending variables, (b) two endogenous structural breaks, and (c) heteroskedastic data series. Our proposed model is applied to a range of time-series, trending, and heteroskedastic energy variables. Our two main findings are: first, the proposed trend-based GARCH unit root model outperforms a GARCH model without trend; and, second, allowing for a time trend and two endogenous structural breaks are important in practice, for doing so allows us to reject the unit root null hypothesis.