Journal of Time Series Analysis

ESTIMATING FINITE SAMPLE CRITICAL VALUES FOR UNIT ROOT TESTS USING PURE RANDOM WALK PROCESSES:A NOTE

Journal Article

Abstract. Finite sample critical values currently available for the augmented Dickey‐Fuller test are commonly obtained via simulations using ARIMA (0, 1, 0) processes. An implicit but critical assumption is that the possible presence of nuisance nonunit roots in general processes does not affect the finite sample size property of the test. The validity of this assumption, though always presumed, has not been verified. This study shows that the use of ARIMA (0, 1, 0) processes for computing the critical values is not so restrictive as it may seem. By estimating empirical size curves as a function of nuisance root parameters, results of Monte Carlo analysis suggest that the empirical test size is not sensitive to nuisance autoregressive (AR) and moving‐average (MA) roots over a wide range of their values, except only when the AR or MA root is near unity. The results support, though not unqualifiedly, the reliability and usefulness of finite sample critical values estimated based on simple ARIMA (0, 1, 0) processes.

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