Residual-Based Tests for the Null of Stationarity with Applications to U.S. Macroeconomic Time Series

In Choi

50 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

This paper proposes residual-based tests for the null of level- and trend-stationarity, which are analogs of the LM test for an MA unit root. Asymptotic distributions of the tests are nonstandard, but they are expressed in a unified manner by expressing stochastic integrals. In addition, the tests are shown to be consistent. By expressing the distributions expressed as a function of a chi-square variable with one degree of freedom, the exact limiting probability density and cumulative distribution functions are obtained, and the exact limiting cumulative distribution functions are tabulated. Finite sample performance of the proposed tests is studied by simulation. The tests display stable size when the lag truncation number for the long-run variance estimation is chosen appropriately. But the power of the tests is generally not high at selected sample sizes. The test for the null of trend-stationarity is applied to the U.S. macroeconomic time series along with the Phillips-Perron Z(⋯) test. For some monthly and annual series, the two tests provide consistent inferential results. But for most series, the two contradictory nulls of trend-stationarity and a unit root cannot be rejected at the conventional significance levels.

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References

1987Co-Integration and Error Correction: Representation, Estimation, and Testing 1988Testing for a Unit Root in Time Series Regression 1992Testing the null hypothesis of stationarity against the alternative of a unit root 1982Trends and random walks in macroeconmic time series 1991Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimation 1980Do Stock Prices Move Too Much to be Justified by Subsequent Changes in Dividends?1987Time Series Regression with a Unit Root 1992An Improved Heteroskedasticity and Autocorrelation Consistent Covariance Matrix Estimator

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2006Panel Unit Root Tests: A Review 1995Testing for Cointegration in a System of Equations 2004STATIONARITY TESTING WITH COVARIATES 1999Testing the null of stationarity for multiple time series 2007Causal relation between interest and exchange rates in the Asian currency crisis 2003Size and Power of Tests for Stationarity in Highly Autocorrelated Time Series

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