Construction of Stationarity Tests with Less Size Distortions

We propose a (trend) stationarity test with a good finite sample size even when a process is (trend) stationary with strong persistence; this is useful for distinguishing between a (trend) stationary process with strong persistence and a unit root process. It could be considered as a modified version of Leybourne and McCabe's test (1994, LMC), but with adi fferent correction method for serial correlation. A Monte Carlo simulation reveals that in terms of empirical size, our test is closer to the nominal one than the original LMC test and is more powerful than the LMC test with size-adjusted critical values.LM test, stationary, unit root

The Rank of a Sub-Matrix of Cointegration

This paper proposes a test of the rank of the sub-matrix of b, where b is a cointegrating matrix. In addition, the sub-matrix of d, an orthogonal complement to b, is investigated. We show that information on the rank of the sub-matrix of b and/or d is useful in several situations. We construct the test statistic by using the eigenvalues of the quadratic form of the sub-matrix. We show that the test statistic has a limiting chi-squared distribution when the data is non-trending, and we propose a conservative test when the data is trending. Finite sample simulations show that, although the simulation settings are limited, the proposed test works well.

Testing the Rank of a Sub-Matrix of Cointegration with a Deterministic Trend

In this paper we consider the test of the rank of the sub-matrix of b, the cointegrating matrix, when the process has a deterministic linear trend. We review the problem of the testing procedure proposed by Kurozumi (2003) and give the alternative test statistic that is symptotically chi-square distributed. We also propose the test of the rank of the sub-matrix of d, the orthogonal matrix to b. Monte Carlo simulations show that our tests proposed in this paper work fairly well in finite samples even when the tests proposed by Kurozumi (2003) perform poorly.

Testing for Multiple Structural Changes with Non-Homogeneous Regressors

This paper investigates tests for multiple structural changes with non-homogeneous regressors, such as polynomial trends. We consider exponential-type, supremum-type and average-type tests as well as the corresponding weighted-type tests suggested in the literature. We show that the limiting distributions depend on regressors in general, and we need to tabulate critical values depending on them. Then, we focus on the linear trend case and obtain the critical values of the test statistics. The Mote Carlo simulations are conducted to investigate the finite sample properties of the tests proposed in the paper, and it is found that the specification of the number of breaks is an important factor for the finite sample performance of the tests. Since it is often the case that we cannot prespecify the number of breaks under the alternative but can suppose only the maximum number of breaks, the weighted-type tests are useful in practice.Multiple Breaks, Exp-type Test, Sup-type Test, Avg-type Test, Mean-type Test

Construction of Stationarity Tests with Less Size Distortions

We propose a (trend) stationarity test with a good finite sample size even when a process is (trend) stationary with strong persistence; this is useful for distinguishing between a (trend) stationary process with strong persistence and a unit root process. It could be considered as a modified version of Leybourne and McCabe's test (1994, LMC), but with a different correction method for serial correlation. A Monte Carlo simulation reveals that in terms of empirical size, our test is closer to the nominal one than the original LMC test and is more powerful than the LMC test with size-adjusted critical values.LM test, stationary, unit root

Testing for the Null Hypothesis of Cointegration with Structural Breaks (Subsequently published in "Econometric Reviews", Volume 26, Issue 6 November 2007, pages 705 - 739. )

In this paper we propose residual-based tests for the null hypothesis of cointegration with structural breaks against the alternative of no cointegration. The Lagrange Multiplier test is proposed and its limiting distribution is obtained for the case in which the timing of a structural break is known. Then the test statistic is extended in two ways to deal with a structural break of unknown timing. The first test statistic, a plug-in version of the test statistic for known timing, replaces the true break point by the estimated one. We also propose a second test statistic where the break point is chosen to be most favorable for the null hypothesis. We show the limiting properties of both statistics under the null as well as the alternative. Critical values are calculated for the tests by simulation methods. Finite-sample simulations show that the empirical size of the test is close to the nominal one unless the regression error is very persistent and that the test rejects the null when no cointegrating relationship with a structural break is present.

A Locally Optimal Test for No Unit Root in Cross-sectionally Dependent Panel Data

This paper develops a simple test for the null hypothesis of no unit root for panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. We show that our test is asymptotically locally optimal, although the optimality is not guaranteed under a wide range of the alternative.KPSS test, unit root, cross-sectional dependence, LM test, locally best test

Tests for Long-Run Granger Non-Causality in Cointegrated Systems

In this paper, we propose a new approach to test the hypothesis of long-run Granger non-causality in cointegrated systems. We circumvent the problem of singularity of the variance-covariance matrix associated with the usual Wald type test by proposing a generalized inverse procedure, and an alternative simple procedure which can be approximated by a suitable chi-square distribution. A test for the ranks of submatrices of the cointegration matrix and its orthogonal matrix plays a vital role in the former. The relevant small sample experiments indicate that the proposed method performs reasonably well in finite samples. As empirical applications, we examine long-run causal relations among long-term interest rates of three and five nations.Vector autoregression, Cointegration, Long-run causality, Hypothesis testing

Model Selection Criteria in Multivariate Models with Multiple Structural Changes

This paper considers the issue of selecting the number of regressors and the number of structural breaks in multivariate regression models in the possible presence of mul- tiple structural changes. We develop a modified Akaike's information criterion (AIC), a modified Mallows' Cp criterion and a modified Bayesian information criterion (BIC). The penalty terms in these criteria are shown to be different from the usual terms. We prove that the modified BIC consistently selects the regressors and the number of breaks whereas the modified AIC and the modified Cp criterion tend to overly choose them with positive probability. The finite sample performance of these criteria is investigated through Monte Carlo simulations and it turns out that our modification is successful in comparison to the classical model selection criteria and the sequential testing procedure with the robust method.structural breaks, AIC, Mallows' Cp, BIC, information criteria

A Simple Panel Stationarity Test in the Presence of Cross-Sectional Dependence

This paper develops a simple test for the null hypothesis of stationarity in heterogeneous panel data with cross-sectional dependence in the form of a common factor in the disturbance. We do not estimate the common factor but mop-up its effect by employing the same method as the one proposed in Pesaran (2007) in the unit root testing context. Our test is basically the same as the KPSS test but the regression is augmented by cross-sectional average of the observations. We also develop a Lagrange multiplier (LM) test allowing for cross-sectional dependence and, under restrictive assumptions, compare our augmented KPSS test with the extended LM test under the null of stationarity, under the local alternative and under the fixed alternative, and discuss the differences between these two tests. We also extend our test to the more realistic case where the shocks are serially correlated. We use Monte Carlo simulations to examine the finite sample property of the augmented KPSS test.Panel data, stationarity, KPSS test, cross-sectional dependence, LM test, locally best test