ABSTRACT
Dickey and Zhang (2010) developed a central limit theorem for seasonal unit root tests based on the studentized coefficient in the regression of Yt − Yt−d on Yt−d when the seasonal period d gets large. They give an easily computable order d−1/2 bias adjustment whose inclusion brings the statistic’s distribution quite close to its N(0, 1) limit for d as small as 4. Their results extend to allow for a fixed number of deterministic regressors, low degree polynomials or sinusoids, e.g., whose inclusion introduces an additional order d−1/2 bias. In the case of such deterministic trend adjustments, their simulations suggest that the number of regressors k must be small relative to d. Cases in which the number of regressors is proportional to d, such as the addition of seasonal dummy variables to the model, are not covered by their theory. This chapter extends the results to include the use of such dummy variables. From existing
K12089 Chapter: 16 page: 383 date: February 14, 2012
K12089 Chapter: 16 page: 384 date: February 14, 2012
Modeling and
unit root tests for seasonal series, Dickey, Hasza, and Fuller (1984), e.g., it is clear that without some adjustment the student t-test for a unit root will not have a standard normal limit. A model for a series that displays regular seasonal behavior should contain some deterministic periodic functions in order for the test to have a chance of concluding that the residuals from the deterministic function are stationary.
