The behaviour of seasonal unit root tests under neglected local drifts

This paper analyses the limit distributions of the seasonal unit root test procedures proposed by Dickey, Hasza and Fuller (1984) and Hylleberg, Engle, Granger and Yoo (1990), when local trends at different frequencies are present in data generation processes, but ignored in the test regressions used. The findings presented explicitly show that neglected deterministic trends have negative effects on the distributions of the test statistics. Analytical observations and Monte Carlo simulations reveal that seasonal unit root test statistics become severely undersized as the values of standardized local trends increase. Hence, failure to consider local trends may often bear the undesirable effect of biasing decisions towards non-rejection of unit roots.Received: February 2001, Accepted: September 2001, JEL Classification: C12, C22Paulo M. M. Rodrigues: I am thankful to two anonymous referees for their detailed and useful comments and suggestions.     

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.     

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.     

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.     

Weighted symmetric tests for a unit root: response functions,power, test dependence and test conflict

The most frequently applied test statistics for a unit root are the Dickey–Fuller tests, which are built into many econometric packages along with MacKinnon's empirical response functions. This article provides empirical response functions for some easy to compute alternative test statistics that are generally much more powerful than the Dickey–Fuller tests; specifically, these are the Dickey–Fuller tests and the weighted symmetric versions of the and tests. The empirical response functions presented here take into account adjustments for lag length in the maintained regression, and also extend the design of the simulation experiments compared to previous work. A second aspect of this study concerns the widespread practice in applied econometrics of using more than one test for the same feature without an assessment of the implications for the cumulative significance level and probability of test conflict. Tests for a unit root being are a leading example of this practice. Using the extended set of unit root tests considered here, the extent of test dependence is simulated and overall type one error calculated. Two empirical applications illustrate the key principles.     

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.     

GLS detrending-based unit root tests in nonlinear STAR and SETAR models

We extend GLS detrending procedure to testing for unit roots against STAR and SETAR alternatives. Monte Carlo simulations and applications to DM/Yen real exchange rates demonstrate that GLS detrending-based nonlinear unit root tests are more powerful than OLS detrending-based counterparts.     

The structure of tourist expenditure in Fiji: evidence from unit root structural break tests

The central aim of this paper is to investigate whether shocks to Fiji's tourism industry have a permanent effect or a transitory effect on tourist expenditure in Fiji. To accomplish this aim the Zivot and Andrews (1992 Zivot, E and Andrews, D. 1992. Further evidence of the great crash, the oil-price shock and the unit-root hypothesis. Journal of Business and Economic Statistics, 10: 251–70.  ) one break test and the Lumsdaine and Papell (1997 Lumsdaine, R and Papell, D. 1997. Multiple trend breaks and the unit root hypothesis. Review of Economics and Statistics, 79: 212–18.  ) two break tests are used. The one break and two break tests reveal 1987 – the year of the military coups in Fiji – as the year of the break. Moreover, it is possible to reject the unit root null leading to the conclusion that shocks to Fiji's tourism industry have a transitory effect on tourist expenditure in Fiji.     

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.     

Performance of LM-type unit root tests with trend break: A bootstrap approach

Using the bootstrap approach, we study the finite-sample properties of the Lagrange Multiplier (LM) unit root tests when level shifts are allowed under the null hypothesis. Bootstrapped critical values support the invariance property of the LM tests. Applying two LM-type tests to the Nelson–Plosser data, we find less evidence against the unit root null than that given by Zivot and Andrews [Zivot, E. and Andrews, D.W.K. (1992), “Further Evidence of the Great Crash, the Oil Price Shock and the Unit Root Hypothesis,” Journal of Business and Economic Statistics 10, 251–270.] when level shifts are allowed under the null.     

Data-dependent selection of the lag truncation parameter in unit root tests of the Phillips-Perron type

The Andrews (Econometrica, 1991, 59, 817–858) plug-in method of heteroscedastic and autocovariance consistent covariance matrix estimation is used to construct estimators of the long-run variance parameter for use in Phillips-Perron unit root tests. This allows the lag truncation parameter to be data dependent. Monte Carlo size and power estimates are obtained suggesting that this apparently natural approach does not provide significant improvements in test performance.     

Nonlinearity and nonstationarity in international art market prices: evidence from Markov-switching ADF unit root tests

This study investigates the presence (or lack thereof) of nonlinear dynamics and nonstationarity in international art market prices using quarterly data for the period 1990–2011. We first test whether art market price indices follow stochastic trends or whether they are stationary by means of linear unit root tests. Next, we estimate the Markov regime-switching ADF model and test whether the linear or the nonlinear regime-switching model provides a better characterization of the global art market price series. We find that all art market price indices (except for Drawings) exhibit nonlinearity. To our knowledge, our study is the first one in the literature to suggest that a nonlinear (Markov regime-switching) model provides a better characterization of the behavior of price dynamics in international art markets. In particular, our findings indicate that the market for the overall global art market, paintings, old masters, sculptures, photographs, prints, and contemporary art might indeed be stationary while exhibiting nonlinear regime-switching properties. On the other hand, the market for drawings and the Nineteenth century art are found to be nonstationary. Overall, despite the common ground of a regime-switching framework, we still find that the sub-segments of the art market have their own inner regime switching dynamics and hence they can evolve differently overtime.     

Asymmetric behavior of inflation differentials in the euro area: Evidence from a threshold unit root test

This paper tests the existence of persistent inflation rate differentials in the euro area by employing linear as well nonlinear unit root tests. Besides linear unit root tests, a two-regime threshold unit root test examines the conjecture that inflation rate differentials follow a nonlinear two-regime process towards a threshold, switching from the persistent regime to the transitory one and vice versa. The results imply that threshold nonlinearity is confirmed in 10 out of the 16 cases. However, we have found unit root regime-switching behavior only in six out of the 16 cases under investigation. This finding implies that these inflation rate differentials were persistent when they were low (regime 1), but transitory when they were high (regime 2). This asymmetric behavior can possibly be explained by the different degree of pressure exercised on governments, which is accompanied with different inflation rate differentials. On the contrary, despite the evidence of nonlinearity, the majority of the inflation rate differentials are found to be monotonically persistent. Our results have strong implications for policy makers. In particular, the documented persistency in the inflation rate differentials might have long-run costs in terms of price and macroeconomic stability.     

IV threshold cointegration tests and the Taylor rule

The usual cointegration tests often entail nuisance parameters that hinder precise inference. This problem is even more pronounced in a nonlinear threshold framework when stationary covariates are included. In this paper, we propose new threshold cointegration tests based on instrumental variables estimation. The newly suggested IV threshold cointegration tests have standard distributions that do not depend on any stationary covariates. These desirable properties allow us to formally test for threshold cointegration in a nonlinear Taylor rule. We perform this analysis using real-time U.S. data for several sample periods from 1970 to 2005. In contrast to the linear model, we find strong evidence of cointegration in a nonlinear Taylor rule with threshold effects. Overall, we find that the Federal Reserve is far more policy active when inflation is high than when inflation is low. In addition, we reaffirm the notion that the response to counteract high inflation was weakest in the 1970s and strongest in the Greenspan era.     

Nonlinear mean-reversion to purchasing power parity: exponential smooth transition autoregressive models and stochastic unit root processes

The purpose of this paper is to show an empirical test of subadditivity based on a sufficient condition-namely, transray convexity coupled with global economies of scale-which has not been commonly used in the literature. We use this sufficient condition to test the hypothesis of subadditivity of the cost function in the largest Portuguese Telecommunications firm, CTT, and find that the market for telecommunications services in Portugal was a natural monopoly in the period analysed.     

The rationality of EIA forecasts under symmetric and asymmetric loss

The United States Energy Information Administration publishes annual forecasts of nationally aggregated energy consumption, production, prices, intensity and GDP. These government issued forecasts often serve as reference cases in the calibration of simulation and econometric models, which climate and energy policy are based on. This study tests for rationality of published EIA forecasts under symmetric and asymmetric loss. We find strong empirical evidence of asymmetric loss for oil, coal and electricity prices as well as natural gas consumption, electricity sales, GDP and energy intensity.     

A simple unit root test against asymmetric STAR nonlinearity with an application to real exchange rates in Nordic countries

Existing tests of the unit root hypothesis against the alternative hypothesis of exponential smooth transition autoregressive (ESTAR) nonlinearity implicitly assume symmetry under the alternative. This paper proposes a simple unit root test against the alternative of symmetric or asymmetric ESTAR nonlinearity. In the event that the unit root hypothesis is rejected, a simple test of symmetric versus asymmetric ESTAR nonlinearity is also proposed. The asymptotic distributions of the test statistics are straightforward to establish and finite-sample performance is studied with Monte Carlo simulations. An empirical application involving the real exchange rates of four Nordic countries against the U.S. dollar illustrates the usefulness of the new tests.     

The seasonal unit root structure in New Zealand Macroeconomic variables

ADF unit root tests are generally applied to macroeconomic data prior to testing theoritical models to ensure that all relevant variables are integrated of the same order. Not only is it important to test that these variables are integrated of the same order but also that a cointegrating relationship exists; failure to do so raise the specture of false inference associated with the spurious regression problem. The seasonal nature of quarterly data adds a further proplem which has generally been overcome by seasonally adjusting the data using procedure such as the census X-11 rather than suppressing it, have attempted to determine whether the seasonal component in each variable exhibits stochastic non-stationary. This paper analysisunit roots in a seasonal setting and compares the recently developed tests for seasonal unit roots as well as the standard augmented Dickey-Fuller zerop frequency unit root tests. Of the variables tested relatively few paper to be integrated at the seasonal frequenciues and, as other studies suggest,determinstic seasonal effects are typically more important than stochastic ones.     

The Polish exchange rate system: A unit root and cointegration analysis

In October 1991 Poland has established a crawling peg regime in which the zloty is tied to a currency basket and devalued with a monthly rate of crawl. If the monetary authorities are successful in defending the crawling peg the basket rate measured in Polish zloty is supposed to be stationary. Furthermore, a stable long-run relationship between the zloty-U.S. dollar rate and the basket's value expressed in U.S. dollar is expected to exist. The results of the unit root and cointegration analysis indicate that the monetary authorities have been able to defend the crawling peg for the sample periods under study, although it seems that not all requirements of the exchange rate regime have been met. The foreign exchange markets, however, have not supported the relationships derived from the crawling peg system after the introduction of the free floating system in April 2000.The final version of this paper has been prepared while I was a Jean Monnet Fellow at the European University Institute. I would like to thank the EUI for the award of the Fellowship and its hospitality. Moreover, I am grateful to Helmut Lütkepohl, Anja Schulz, Ralf Brüggemann, and two anonymous referees for many helpful comments and suggestions. I also thank the Deutsche Forschungsgemeinschaft, SFB 373, for financial support.     

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.