PRACTITIONERS CORNER: Lag Order and Critical Values of a Modified Dickey‐Fuller Test
| Date | 01 August 1995 |
| Author | Yin‐Wong Cheung,Kon S. Lai |
| Published date | 01 August 1995 |
| DOI | http://doi.org/10.1111/j.1468-0084.1995.mp57003008.x |
OXFORD BULLETIN OF ECONOMICS AND STATISTICS, 57,3(1995)
0305-9049 $3.00
PRACTITIONERS CORNER
Lag Order and Critical Values of a Modified
Dickey-Fuller Test
Yin- Wong Cheung and Kon £ Lai
I. INTRODUCTION
Unit-root nonstationarity in economic time series has been a hotly contested
issue. A widely used unit-root is the augmented Dickey-Fuller or ADF test
(Dickey and Fuller (1979)). Derived from an autoregressive AR(p + 1)
representation, the test examines the null hypothesis of a unit root against
stationary alternatives. Since the null hypothesis maintained is a
nonstationary process, empirical failures to find stationarity may reflect the
power of the test.
Elliott, Rothenberg, and Stock (1992) devise a new unit-root test with
good power. In studying the asymptotic power envelope for various unit-root
tests, these authors propose a simple modification of the ADF test such that
the modified test, referred to as the DF-GLS test, can nearly achieve the
power envelope. The DF-GLS test is shown to be approximately uniformly
most power invariant (UMPI) while no strictly UMPI test exists. Monte Carlo
results reported indicate that the power improvement from using the
modified Dickey-Fuller test can be large. Elliot, Rothenberg, and Stock
(1992) derive the limiting distribution of the test with and without a time
trend. Approximate finite-sample critical values for the test with a time trend
are tabulated for several sample sizes based on p = O.
The purpose of this study is twofold. First, it demonstrates the significant
effect of lag order on finite-sample critical values of the DF-GLS test.
Empirical applications of the test necessarily deal with finite samples. The
result here suggests that a same set of critical values should not be applied to
tests with different values of p. Second, the study provides estimates of finite-
sample critical values that correct for the effect of lag order. Lag-adjusted
critical values can be computed directly from response surface equations.
The response surface analysis is useful in that it yields estimates of critical
values not only for a few specific sample sizes but a full range of sample sizes.
Response surface analysis has been used by MacKinnon (1991) to obtain
approximate finite-sample critical values for the conventional ADF test. In
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