Testing for (common) stochastic trends in the presence of structural breaks

This paper considers the problem of testing for the presence of stochastic trends in multivariate time series with structural breaks. The breakpoints are assumed to be known. The testing framework is the multivariate locally best invariant test and the common trend test of Nyblom and Harvey (2000). The asymptotic distributions of the test statistics are derived under a specification of the deterministic component which allows for structural breaks. Asymptotic critical values are provided for the case of a single breakpoint. A modified statistic is then proposed, the asymptotic distribution of which is independent of the breakpoint location and belongs to the Cramer-von Mises family. This modification is particularly advantageous in the case of multiple breakpoints. It is also shown that the asymptotic distributions of the test statistics are unchanged when seasonal dummy variables and/or weakly dependent exogenous regressors are included. Finally, as an example, the tests are applied to UK macroeconomic data and to data on road casualties in Great Britain. Copyright © 2002 by John Wiley & Sons, Ltd.

[1]  P. Phillips,et al.  A Primer on Unit Root Testing , 1998 .

[2]  P. Perron,et al.  The Great Crash, The Oil Price Shock And The Unit Root Hypothesis , 1989 .

[3]  Lawrence J. Christiano,et al.  Searching for a Break in Gnp , 1988 .

[4]  Ian B. MacNeill,et al.  Properties of Sequences of Partial Sums of Polynomial Regression Residuals with Applications to Tests for Change of Regression at Unknown Times , 1978 .

[5]  D. Andrews.  Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation , 1991 .

[6]  J. Bai,et al.  Least squares estimation of a shift in linear processes , 1994 .

[7]  Jukka Nyblom.  Testing for Deterministic Linear Trend in Time Series , 1986 .

[8]  Siem Jan Koopman,et al.  Stamp 5.0 : structural time series analyser, modeller and predictor , 1996 .

[9]  In Choi,et al.  Testing for Cointegration in a System of Equations , 1995, Econometric Theory.

[10]  Andrew Harvey,et al.  Testing for the Presence of a Random Walk in Series with Structural Breaks , 1998 .

[11]  S. Johansen.  Estimation and Hypothesis Testing of Cointegration Vectors in Gaussian Vector Autoregressive Models , 1991 .

[12]  J. Stock,et al.  Recursive and Sequential Tests of the Unit Root and Trend Break Hypothesis: Theory and International Evidence , 1990 .

[13]  T. W. Anderson,et al.  Asymptotic Theory of Certain "Goodness of Fit" Criteria Based on Stochastic Processes , 1952 .

[14]  Bruce E. Hansen,et al.  Residual-based tests for cointegration in models with regime shifts , 1996 .

[15]  Yongcheol Shin,et al.  On stationary tests in the presence of structural breaks , 1997 .

[16]  A. C. Harvey,et al.  The Effects of Seat Belt Legislation on British Road Casualties: A Case Study in Structural Time Series Modelling , 1986 .

[17]  Andrew Harvey,et al.  TESTS OF COMMON STOCHASTIC TRENDS , 2000, Econometric Theory.

[18]  J. Bai,et al.  Estimation of a Change Point in Multiple Regression Models , 1997, Review of Economics and Statistics.

[19]  P. Perron,et al.  Nonstationarity and Level Shifts With an Application to Purchasing Power Parity , 1992 .

[20]  P. Phillips,et al.  Testing the null hypothesis of stationarity against the alternative of a unit root: How sure are we that economic time series have a unit root? , 1992 .

[21]  J. Nyblom,et al.  Comparisons of Tests for the Presence of Random Walk Coefficients in a Simple Linear Model , 1983 .

[22]  Calyampudi Radhakrishna Rao,et al.  Linear Statistical Inference and its Applications , 1967 .

[23]  Seiji Nabeya,et al.  Asymptotic Theory of a Test for the Constancy of Regression Coefficients Against the Random Walk Alternative , 1988 .

[24]  S. Johansen.  STATISTICAL ANALYSIS OF COINTEGRATION VECTORS , 1988 .

[25]  P. Phillips.  Time series regression with a unit root , 1987 .

[26]  D. Andrews,et al.  Further Evidence on the Great Crash, the Oil-Price Shock, and the Unit-Root Hypothesis , 1992 .

[27]  Andrew Harvey,et al.  Forecasting, Structural Time Series Models and the Kalman Filter , 1990 .

[28]  P. Perron,et al.  Testing for a Unit Root in a Time Series with a Changing Mean: Corrections and Extensions , 1992 .

[29]  Atsushi Inoue.  Tests of cointegrating rank with a trend-break , 1999 .

[30]  L. A. Gardner.  On Detecting Changes in the Mean of Normal Variates , 1969 .

[31]  P. Perron,et al.  Further Evidence on Breaking Trend Functions in Macroeconomic Variables. , 1997 .

[32]  P. Schmidt,et al.  On the Power of the KPSS Test of Stationarity Against Fractionally-Integrated Alternatives , 1996 .

[33]  Harald Uhlig,et al.  Reasonable extreme bounds analysis , 1990 .

[34]  J. Nyblom.  Testing for the Constancy of Parameters over Time , 1989 .