Range unit root tests

Since the seminal paper by Dickey and Fuller in 1979, unit-root tests have conditioned the standard approaches to analyse time series with strong serial dependence, the focus being placed in the detection of eventual unit roots in an autorregresive model fitted to the series. In this paper we propose a completely different method to test for the type of "long-wave" patterns observed not only in unit root time series but also in series following more complex data generating mechanism. To this end, our testing device analyses the trend exhibit by the data, without imposing any constraint on the generating mechanism. We call our device the Range Unit Root (RUR) Test since it is constructed from running ranges of the series. These statistics allow a more general characterization of a strong serial dependence in the mean behavior, thus endowing our test with a number of desirable properties. Among these properties are the invariance to nonlinear monotonic transformations of the series and the robustness to the presence of level shifts and additive outliers. In addition, the RUR test outperforms the power of standard unit root tests on near-unit-root stationary time series

Unit root testing

The occurrence of unit roots in economic time series has far reaching consequences for univariate as well as multivariate econometric modelling. Therefore, unit root tests are nowadays the starting point of most empirical time series studies. The oldest and most widely used test is due to Dickey and Fuller (1979). Reviewing this test and variants thereof we focus on the importance of modelling the deterministic component. In particular, we survey the growing literature on tests accounting for structural shifts. Finally, further applied aspects are addressed how to get the size correct and obtain good power at the same time. --Dickey-Fuller,size and power,deterministic components,structural breaks

Nonlinear Mean Reversion across National Stock Markets: Evidence from Emerging Asian Markets

This paper seeks empirical evidence of nonlinear mean-reversion in relative national stock price indices for Emerging Asian countries. It is well known that conventional linear unit root tests suffer from low power against the stationary nonlinear alternative. Implementing the nonlinear unit root tests proposed by Kapetanios, et al. (2003) and Cerrato, et al. (2009) for the relative stock prices of Emerging Asian markets, we find strong evidence of nonlinear mean reversion, whereas linear tests fail to reject the unit root null for most cases. We also report some evidence that stock markets in China and Taiwan are highly localized.Linear Unit Root Test; Nonlinear Unit Root Test; Nonlinear Panel Unit Root Test; International Relative Stock Prices

ARE SHOCKS TO ENERGY CONSUMPTION PERMANENT OR TEMPORARY? EVIDENCE FROM 182 COUNTRIES

This paper applies univariate and panel data unit root tests to annual panel data for 182 countries over the period 1979-2000 to examine the stationarity properties of per capita energy consumption. The univariate unit root test can only reject the unit root null for 29 per cent of the countries at the 10 per cent level or better without a trend and 37 per cent of the countries at the 10 per cent level or better with a trend. However, it is often argued that unit root tests have low power with short spans of data and therefore failure to reject the unit root null should be treated with caution. When we apply the panel data unit root test we find overwhelming evidence that energy consumption is stationary. We discuss the implications of these findings for econometric modeling and policy formulation.Energy consumption, Unit roots, Panel data

Bootstrap Unit Root Tests

We consider the bootstrap unit root tests based on autoregressive integrated models, with or without deterministic time trends. A general methodology is developed to approximate asymptotic distributions for the models driven by integrated time series, and used to obtain asymptotic expansions for the Dickey-Fuller unit root tests. The second-order terms in their expansions are of stochastic orders Op($n^{-1/4}$) and Op($n^{-1/2}$), and involve functionals of Brownian motions and normal random variates. The asymptotic expansions for the bootstrap tests are also derived and compared with those of the Dickey-Fuller tests. We show in particular that the usual nonparametric bootstrap offers asymptotic refinements for the Dickey-Fuller tests, i.e., it corrects their second-order errors. More precisely, it is shown that the critical values obtained by the bootstrap resampling are correct up to the second-order terms, and the errors in rejection probabilities are of order o($n^{-1/2}$) if the tests are based upon the bootstrap critical values. Through simulation, we investigate how effective is the bootstrap correction in small samples.

Unit Roots, Level Shifts and Trend Breaks in Per Capita Output: A Robust Evaluation

Determining whether per capita output can be characterized by a stochastic trend is complicated by the fact that infrequent breaks in trend can bias standard unit root tests towards non-rejection of the unit root hypothesis. The bulk of the existing literature has focused on the application of unit root tests allowing for structural breaks in the trend function under the trend stationary alternative but not under the unit root null. These tests, however, provide little information regarding the existence and number of trend breaks. Moreover, these tests su¤er from serious power and size distortions due to the asymmetric treatment of breaks under the null and alternative hypotheses. This paper estimates the number of breaks in trend employing procedures that are robust to the unit root/stationarity properties of the data. Our analysis of the per-capita GDP for OECD countries thereby permits a robust classi?cation of countries according to the ?growth shift?, ?level shift? and ?linear trend? hypotheses. In contrast to the extant literature, unit root tests conditional on the presence or absence of breaks do not provide evidence against the unit root hypothesis.growth shift, level shift, structural change, trend breaks, unit root

Are Shocks to Commodity Prices Persistent?

This paper considers the issue of whether shocks to ten commodity prices (gold, silver, platinum, copper, aluminum, iron ore, lead, nickel, tin, and zinc) are persistent or transitory. We use two recently developed unit root tests, namely the Narayan and Popp (NP, 2010) test and the Liu and Narayan (LN, 2010) test that allow for two structural breaks in the data series. Using the NP test, we are able to reject the unit root null for iron ore and tin, while, using the GARCH-based unit root test of LN, we are able to reject the unit root null for five commodity prices; namely, iron ore, nickel, zinc, lead, and tin. Our findings, thus, suggest that only shocks to gold, silver, platinum, aluminum, and copper are persistent.Commodity Prices; Unit Root Test; GARCH.

An Improved Panel Unit Root Test Using GLS-Detrending

We propose to combine recent developments in univariate and mul- tivariate unit root testing in order to construct a more powerful panel unit root test. We extend the GLS-detrending procedure of Elliott, Rothenberg and Stock (1996) to a panel Augmented Dickey-Fuller test. The .nite sample power properties of the new test demonstrate a very large gain when compared to existing tests, especially for small panels. We then investigate the topic of Purchasing Power Parity for the post Bretton-Woods period via this new test. The results show strong rejections of the unit root hypothesis.DF-GLS, panel unit root