A TEST FOR STATIONARITY VERSUS TRENDS AND UNIT ROOTS FOR A WIDE CLASS OF DEPENDENT ERRORS

Liudas Giraitis · Remigijus Leipus · Anne Philippe

40 citations0/0 files storedEconometric Theory

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Monetary Policy and Economic Impact Complex Systems and Time Series Analysis Diverse Scientific and Economic Studies

Abstract

We suggest a rescaled variance type of test for the null hypothesis of stationarity against deterministic and stochastic trends (unit roots). The deterministic trend can be represented as a general function in time (e.g., nonparametric, linear, or polynomial regression, abrupt changes in the mean). Under the null, the asymptotic distribution of the test is derived, and critical values are tabulated for a wide class of stationary processes with short, long, or negative dependence structure. A simulation study examines the performance of the test in terms of size and power. The empirical performance of the test is illustrated using the S&P 500 data.The authors thank the editor, the referees, and Karim Abadir for helpful comments and Alfredas Račkauskas for drawing our attention to the criterion of Cremers and Kadelka (1986). The first author's work was supported by the ESRC grants R000238212 and R000239538. The last two authors were supported by a cooperation agreement CNRS/LITHUANIA (4714) and by a bilateral Lithuania-France research project Gilibert.

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References

1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1992Testing the null hypothesis of stationarity against the alternative of a unit root 1989The Great Crash, the Oil Price Shock, and the Unit Root Hypothesis 1982Trends and random walks in macroeconmic time series 1993Tests for Parameter Instability and Structural Change With Unknown Change Point 1999Unit Roots, Cointegration, and Structural Change 1991Long-Term Memory in Stock Market Prices 1995Gaussian Semiparametric Estimation of Long Range Dependence

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