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ABSTRACT: This paper introduces a new test statistic for the null hypothesis of short memory against long memory alternatives. The novelty of our statistic is that it is based on only high-order sample autocovariances and by construction eliminates the effects of nuisance parameters typically induced by short memory autocorrelation. For practically relevant situations where the short memory process is not directly observed, but instead appears as the disturbance term in a deterministic linear regression model, we are able to demonstrate that our residual-based statistic has an asymptotic standard normal distribution under the null hypothesis. We also establish consistency of the statistic under long memory alternatives. The finite-sample properties of our procedure are compared to other well-known tests in the literature via Monte Carlo simulations. These show that the empirical size properties of the new statistic can be very robust compared to existing tests and also that it competes well in terms of power.We thank the associate editor and two anonymous referees for their valuable comments on an earlier draft of this paper.
Econometric Theory 02/2008; 24(01):143-175. · 0.86 Impact Factor
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ABSTRACT: This note suggests a simple modification to the Kwiatkowski, Phillips, Schmidt, and Shin (1992, Journal of Econometrics, 54, 159 178) test (KPSS test) so that it is applicable to testing the null hypothesis of near integration against a unit root alternative. The modified KPSS test is shown not to suffer from the asymptotic size distortion problems of the original KPSS test that are described by M ller (2005, Journal of Econometrics 128, 195 213). The test also has good asymptotic and finite-sample properties relative to the point optimal tests of M ller (2005) and Elliott and M ller (2006, Journal of Econometrics 135, 285 310).
Econometric Theory 01/2007; 23(02):355-363. · 0.86 Impact Factor
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ABSTRACT: We consider the problem of hypothesis testing in a modified version of the stochastic integration and cointegration framework of Harris, McCabe, and Leybourne (2002, Journal of Econometrics 111, 363 384). This nonlinear setup allows for volatility in excess of that catered for by the standard integration cointegration paradigm through the introduction of nonstationary heteroskedasticity. We propose a test for stochastic cointegration against the alternative of no cointegration and a secondary test for stationary cointegration against the heteroskedastic alternative. Asymptotic distributions of these tests under their respective null hypotheses are derived, and consistency under their respective alternatives is established. Monte Carlo evidence suggests that the tests will perform well in practice. An empirical application to the term structure of interest rates is also given.We are most grateful to the Associate Editor and two anonymous referees for providing helpful comments on earlier versions of this paper.
Econometric Theory 01/2006; 22(03):429-456. · 0.86 Impact Factor
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Journal of Business and Economic Statistics 02/2005; 23(October):395-409. · 1.78 Impact Factor
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ABSTRACT: Using the stochastic integration/cointegration framework of Harris, McCabe and Leybourne (2002) we revisit the problem of assessing the empirical evidence for or against the present value class of models in the bond and stock markets. This framework allows for volatility in excess of that catered for by the conventional integration/cointegration paradigm by introducing nonlinear heteroscedasticity. We propose a test for stochastic cointegration against the alternative of no cointegration and a secondary test for stationary cointegration against the heteroscedastic alternative. Asymptotic distributions of these tests under their respective null hypotheses are derived and consistency under their respective alternatives is established. In contrast to conventional cointegration tests, which we show via simulation are unreliable in the presence of the kind of volatility typical of financial data, our tests are able to uncover new cointegration evidence in favour of the present value model, particularly in the bond market.
12/2003;
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ABSTRACT: We present a test of the null hypothesis of stationarity against unit root alternatives for panel data that allows for arbitrary cross- sectional dependence. We treat the short run time series dynamics non- parametrically and thus avoid the need to fit separate models for the individual series. The statistic is simple to compute and is asymptotically normally distributed, even in the presence of a wide range of deterministic components. Taken together, these features provide a generally applicable solution to the problem of testing for stationarity versus unit roots in macro-panel based data. The test is applied to assess the validity of the purchasing power parity hypothesis and finds significant evidence against the hypothesis being true.
12/2003;
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ABSTRACT: In this paper we provide some weak convergence results for sample statistics of the product of a variable with its kth-order lag. We assume the variable is a stationary vector that can be represented by linear process, and the lag length k is allowed to be a function of the sample size. Employing the Beveridge Nelson decomposition, we derive a new functional central limit theorem for this situation and establish related stochastic integral convergence results. We then consider the behavior of associated long-run variance estimators and also extend our analysis to the case where the sample statistics are based on regression residuals. We illustrate the potential range of application of these techniques in the context of (i) testing for I(0) versus I(1) behavior and (ii) estimation and testing in a heteroskedastically cointegrated regression model.We thank the co-editor and the referees for helpful comments on earlier drafts.
Econometric Theory 02/2003; 19(05):829-864. · 0.86 Impact Factor
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Journal of Econometrics. 02/2002; 111(2):363-384.
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ABSTRACT: The authors describe some simple methods for improving the performance of stationarity tests (i.e., tests that have a stationary null and a unit-root alternative). Specifically, they increase the rate of convergence of the test under the unit-root alternative from O-N9-p(T) to O-N9-p(T-N9-2), then suggest an optimal method of selecting the order of the autoregressive component in the fitted autoregressive integrated moving average model on which the test is based. Simulation evidence suggests that these modifications work well. The authors apply the modified procedure to U.S. monthly macroeconomic data and uncover new evidence of a unit root in unemployment.
Journal of Business and Economic Statistics 02/1999; 17(2):264-70. · 1.78 Impact Factor
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ABSTRACT: This paper considers a class of nonstationary varying coefficient autoregressive models which allow stochastic variability in the autoregressive root. It is argued that such models provide a better description of the behaviour of macroeconomic variables than fixed unit root autoregressive models as they allow more general forms of nonstationarity. We construct a test of the null hypothesis of a fixed unit root against the alternative of a fixed unit root against the alternative of a randomized root with unit mean, and derive its asymptotic distribution. The test is applied to a number of U.S. macroeconomic series generally considered to contain fixed unit roots. We find that for about half of the series the fixed unit root null is rejected.
Journal of Business and Economic Statistics 02/1996; 14(4):435-46. · 1.78 Impact Factor
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ABSTRACT: This note proposes a simple test for cointegration in which, unlike conventional test procedures, the presence of cointegration forms the null hypothesis to be tested. The test statistic is constructed under the assumption of normality and then it's asymptotic distribution is derived under considerably more general conditions. Selected critical values of this distribution, computed from Monte Carlo simulations, are presented. Copyright 1994 by Blackwell Publishing Ltd
Oxford Bulletin of Economics & Statistics 02/1994; 56(1):97-103. · 1.00 Impact Factor
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ABSTRACT: This article investigates several U.S. macroeconomic time series for the presence of a unit root using a newly developed test. This test has stationarity as its null hypothesis and the alternative is a unit-root process. The test is shown to be consistent and its asymptotic null distribution is determined. The authors' findings contrast sharply with those obtained via the standard unit-root tests.
Journal of Business and Economic Statistics 02/1994; 12(2):157-66. · 1.78 Impact Factor
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ABSTRACT: This article is concerned with Locally Best Invariant tests for coefficient stability in a univariate random walk coefficient regression model. In particular, we explore the effects that different assumptions about the initial value of the random walk process have on the form and asymptotic distribution of the resulting test statistics. When this initial value is allowed to be random, it is shown that the test statistics are either exactly the same, or possess the same asymptotic distributions, as when the initial value is fixed.
Empirical Economics 02/1989; 14(2):105-12. · 0.60 Impact Factor
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Journal of the Royal Statistical Society Series B. 73(2):253-272.
