Purchasing power parity in OECD countries: Nonlinear unit root tests revisited

The aim of this paper is to provide additional evidence on the purchasing power parity empirical fulfilment in a pool of OECD countries. We apply the Harvey et al. (2008) linearity test and the Kruse (2011) nonlinear unit root test. The results point to the fact that the purchasing power parity theory holds in a greater number of countries than has been reported in previous studies.     

Effects of data aggregation on the power of tests for a unit root : A simulation study

This paper studies the effects of data aggregation on the powers of the Phillips-Perron and augmented Dickey-Fuller tests for a unit root by simulation. It is shown that using the data generated by aggregating subinterval data results in lower powers of the tests. In addition, especially for the aggregate data, the Phillip-Perron tests appear to be more powerful than the augmented Dickey-Fuller test in finite samples, according to our experimental format.     

Panel unit root tests under cross section dependence with recursive mean adjustment

Utilizing recursive mean adjustment (RMA) we provide two unit root tests: the covariate RMA unit root test and the panel feasible generalized RMA unit root test. The proposed panel unit root tests are precise and powerful, especially when T > N.     

The power of asymmetric unit root tests under threshold and consistent-threshold estimation

The asymmetric unit root tests of Enders and Granger (Journal of Business and Economic Statistics, 16, 304–11, 1998) are examined using consistent threshold estimation and the original two-step procedure. In contrast to earlier studies, the ability of the tests to jointly reject the unit root and symmetry hypotheses is examined, thus permitting a fuller analysis of the tests' properties. Whilst the threshold autoregressive test is found to have little power in either its consistent or original forms, the consistent momentum-threshold autoregressive test is found to exhibit high power against a range of plausible alternatives when using newly derived critical values.     

Asymptotic behaviour of tests for a unit root against an explosive alternative

We compare the asymptotic local power of upper-tail unit root tests against an explosive alternative based on ordinary least squares (OLS) and quasi-differenced (QD) demeaning/detrending. We find that under an asymptotically negligible initialisation, the QD-based tests are near asymptotically efficient and generally offer superior power to OLS-based approaches; however, the power gains are much more modest than in the lower-tail testing context. We also find that asymptotically non-negligible initial conditions do not affect the power ranking in the same way as they do for lower-tail tests, with the QD-based tests retaining a power advantage in such cases.     

Regime-switching purchasing power parity in Latin America: Monte Carlo unit root tests with dynamic conditional score

We suggest a Monte Carlo simulation-based unit root test of the purchasing power parity theory for Latin American countries. Under the null hypothesis, we use a Markov regime-switching (MS) model with unit root in the conditional location and MS volatility dynamics. Under the alternative hypothesis, the proposed test incorporates Markov regime-switching autoregressive moving average (MS-ARMA) plus MS volatility dynamics. Under both the null and alternative hypotheses, one of the volatility models estimated is Beta-t-EGARCH, which is a recent dynamic conditional score volatility model. We use data on real effective exchange rate time series for 14 Latin American countries. For each country, we estimate by Monte Carlo simulation the critical values of the unit root test. We provide an economic discussion of the unit root test results and also study the robustness of MS-ARMA plus MS volatility with respect to smooth transition autoregressive models with Fourier function.     

The Phillips unit root tests for polynomials of integrated processes

In this paper, we derive the limiting distributions of the first order serial correlation coefficient and its t-statistic, which are the basis for the non-parametric unit root tests of Phillips (1987), for polynomials of integrated processes. The resulting limiting distributions depend upon nuisance parameters and in general the modification proposed by Phillips (1987), to achieve a nuisance parameter free limiting distribution, is not feasible for polynomials of integrated processes. For the special case of serially uncorrelated innovations, the limiting distributions are nuisance parameter free and are simulated. The distributions shift to the left with increasing variance for increasing polynomial orders.     

Some cautions on the use of nonlinear panel unit root tests: Evidence from a modified series-specific non-linear panel unit-root test

The purpose of this paper is to examine the relevance of applying nonlinear panel unit root test to examine the non-linear mean reversion behaviors of real exchange rates. We find that nonlinear panel unit root test may achieve lower power performance as compared to its alternative of linear panel unit test when the data generating process does not contain significant non-linear components. This finding post cautions to researchers in modeling and testing real exchanges behavior. We also develop a modified series-specific nonlinear panel unit root test and find evidence in favor of purchasing power parity hypothesis for China's four ASEAN trading partners in the period of February 1997 to August 2009.     

Panel LM unit root tests with level and trend shifts

This paper considers a Lagrange multiplier (LM) based panel unit root test that allows for heterogeneous structural breaks in both the intercepts and slopes of a series. We note that many popular time series variables are likely to exhibit changing means and/or trends over time. Given that the usual tests will depend on the nuisance parameters indicating the locations of the trend breaks, we adopt a transformation procedure that makes our new panel unit root tests invariant to the nuisance parameters. To illustrate the importance of the power gain provided by our test, we examine the convergence hypothesis using relative ratios of per capita health care expenditures in 20 OECD countries. Our results provide evidence that the convergence hypothesis is supported.     

Specification sensitivities in the Markov-switching unit root test for bubbles

The aim of this article is to provide some empirical guidelines for the practical implementation of the Markov-switching augmented Dickey–Fuller (MSADF) test proposed by Hall et al. (J Appl Econom 14:143–154, 1999) for detecting explosive bubble behavior. We conduct simulation studies to compare the performance of the MSADF test under different error variance specifications, namely the constant variance and regime-dependent variance assumptions. An empirical application to the money base, consumer price and exchange rate in Argentina reveals the practical importance of the error variance specification on the MSADF test outcomes.     

Flexible Fourier unit root test of unemployment for PIIGS countries

In this empirical study, we apply the flexible Fourier unit root test proposed by Enders and Lee (2012) to re-examine the hysteresis hypothesis of unemployment for PIIGS (Portugal, Ireland, Italy, Greece, and Spain) countries over the period from 1960 to 2011. We find that the Fourier unit root test has greater power than a linear method if the true data generating process of unemployment is a stationarity, non-linear process of an unknown form with structural change. The hysteresis in unemployment is confirmed for all PIIGS countries, with the exception of Portugal and Spain, when the Fourier unit root test is conducted.     

Stochastic unit root processes: Maximum likelihood estimation,and new Lagrange multiplier and likelihood ratio tests

We show in this study that the maximum likelihood estimators of stochastic unit root (STUR) processes are consistent and asymptotically normally distributed. We also present two new tests for STUR. We first propose a Lagrange multiplier test and show that it has a standard χ² distribution asymptotically. We also propose a likelihood ratio test and show that it has an asymptotic distribution of 50–50 mixture of χ² and a point mass at 0. As an empirical example, we test the existence of STUR in the Canadian real exchange rate and explore the implication of STUR on the validity of purchasing power parity.     

Quantile unit root test and the PPP in Africa

In 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).     

Re-examining the real interest rate parity hypothesis (RIPH) using panel unit root tests with asymmetry and cross-section dependence

This paper investigates the validity of the real interest rate parity hypothesis (RIPH) using a panel unit root approach. For this purpose, first we estimate the possible nonlinear data-generating processes of the real interest rate differential series and using these estimates determine which panel unit root test is better for analyzing the RIPH. To this end, smooth transition autoregressive and threshold autoregressive (TAR) models are estimated for two different panels of countries: G7 and post-Soviet transition economies. The results show that the data displays both strong asymmetry and high transition speed. Therefore, secondly, we propose a new panel unit root test where the alternative is stationary with asymmetric TAR adjustment, and provide their empirical power properties. Finally, we demonstrate that our newly proposed test is able to provide conclusive evidence in favor of the RIPH in contrast to the other panel unit root tests considered.     

An application of a new seasonal unit root test to inflation

In this paper, we apply the modified seasonal unit root test with seasonal level shifts at unknown time proposed by Popp (2007) to the G7 inflation rate. We also study the power properties of this test and generate critical values for a range of different break points and sample sizes. We find that there is a non-seasonal unit root in Canada's inflation rate, a semi-annual unit root in Germany's inflation rate, and no seasonal unit root at the annual frequency for any of the G7 countries.     

Non-linear quantile unit root test and PPP: more evidence from Africa

It is now a common practice to establish stationarity of the real exchange rate as a sign of purchasing power parity (PPP) hypothesis. In this article, we consider the real effective exchange rates of 29 African countries. When we apply conventional linear unit root tests, we find support for the PPP in eight countries. However, when we shift to the newly introduced non-linear quantile unit root test, support for the PPP increases to 15 countries.     

Nonlinear adjustment in the forward premium: evidence from a threshold unit root test

This paper considers testing the mean reversion of the forward premium in a nonlinear framework. In contrast to previous studies, we consider a novel approach that allows for testing for a unit root in the forward premium while explicitly allowing for nonlinearity in the data. Within this approach, we employ bootstrap methods based on threshold autoregressive (TAR) models to investigate whether the 1- and 3-month forward premia for six industrialized countries are mean-reverting. Overall, we are able to reject the null hypotheses of linearity and nonstationarity indicating nonlinear mean reversion. Furthermore, large deviations of the forward premium from its equilibrium band are found to have faster speed of mean reversion than small deviations, which are strongly persistent. In all, the results support the view that the forward premium exhibits mean reversion, but in a special manner not captured by the usual linear tests. Finally, the results have important implications for foreign exchange market efficiency under risk aversion.     

Covariate unit root tests under structural change and asymmetric STAR dynamics

In this paper, we intend to develop a new unit root testing procedure. The novelty of this methodology includes (1) accommodating possible trend breaks of unknown number, unknown dates, and unknown form by employing the Fourier form without directly estimating such breaks; (2) considering possible asymmetric STAR adjustments under the alterative; and (3) utilizing related covariates to boost the testing power. The limiting distribution of the test is derived, and the asymptotic critical values are tabulated. Simulation experiments show that the test can deliver robust size for various breaks commonly seen in economic analysis and enjoy high power property, even in small sample sizes encountered in empirical studies. The usefulness of the test is illustrated in an empirical study on the issue of debt sustainability in 18 OECD countries.