Asymptotic Distributions of Unit-Root Tests When the Process Is Nearly Stationary

Sastry Gouripathi Pantula

78 citations0/0 files storedJournal of Business and Economic Statistics

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Monetary Policy and Economic Impact Time Series Analysis and Forecasting Diverse Scientific and Economic Studies

Abstract

Several test criteria are available for testing the hypothesis that the autoregressive polynomial of an autoregressive moving average process has a single unit root. Schwert (1989), using a Monte Carlo study, investigated the performance of some of the available test criteria. He concluded that the actual levels of the test criteria considered in his study are far from the specified levels when the moving average polynomial also has a root close to 1. This article studies the asymptotic null distribution of the test statistics for testing p = 1 in the model Yt = pY t-1 + e t – 0e t-1 as 0 approaches 1. It is shown that the test statistics differ from one another in their asymptotic properties depending on the rate at which 0 converges to 1.

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References

1979Distribution of the Estimators for Autoregressive Time Series with a Unit Root 1988Testing for a Unit Root in Time Series Regression 1984Testing for Unit Roots in Autoregressive-Moving Average Models of Unknown Order 1987Time Series Regression with a Unit Root 1988Trends and random walks in macroeconomic time series 1988Tests For Unit Roots: A Monte Carlo Investigation 1987Towards a Unified Asymptotic Theory for Autoregression 1987Effects of model specification on tests for unit roots in macroeconomic data

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