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HEGY Tests in the Presence of Moving Averages *
Author(s) -
Castro Tomás Del Barrio,
Osborn Denise R.
Publication year - 2011
Publication title -
oxford bulletin of economics and statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.131
H-Index - 73
eISSN - 1468-0084
pISSN - 0305-9049
DOI - 10.1111/j.1468-0084.2011.00633.x
Subject(s) - autoregressive model , unit root , statistic , monte carlo method , mathematics , statistics , econometrics , null hypothesis , test statistic
We analyze the asymptotic distributions associated with the seasonal unit root tests of Hylleberg et al. (1990) for quarterly data when the innovations follow a moving average process. Although both the t ‐ and F ‐type tests suffer from scale and shift effects compared with the presumed null distributions when a fixed order of autoregressive augmentation is applied, these effects disappear when the order of augmentation is sufficiently large. However, as found by Burridge and Taylor (2001) for the autoregressive case, individual t ‐ratio tests at the semi‐annual frequency are not pivotal even with high orders of augmentation, although the corresponding joint F ‐type statistic is pivotal. Monte Carlo simulations verify the importance of the order of augmentation for finite samples generated by seasonally integrated moving average processes.