TY - JOUR
T1 - Locally Optimal Tests Against Seasonal Unit Roots
AU - Taylor, Anthony
PY - 2003/9/1
Y1 - 2003/9/1
N2 - This paper builds on the existing literature on tests of the null hypothesis of deterministic seasonality in a univariate time-series process. Under the assumption of independent Gaussian errors, we derive the class of locally weighted mean most powerful invariant tests against unit roots at the zero and/or seasonal frequencies in a seasonally observed process. Representations for the limiting distributions of the proposed test statistics under sequences of local alternatives are derived, and the relationship with tests for corresponding moving average unit roots is explored. We also propose nonparametric modifications of these test statistics designed to have limit distributions which are free of nuisance parameters under weaker conditions on the errors. Our tests are shown to contain existing stationarity tests as special cases and to extend these tests in a number of useful directions.
AB - This paper builds on the existing literature on tests of the null hypothesis of deterministic seasonality in a univariate time-series process. Under the assumption of independent Gaussian errors, we derive the class of locally weighted mean most powerful invariant tests against unit roots at the zero and/or seasonal frequencies in a seasonally observed process. Representations for the limiting distributions of the proposed test statistics under sequences of local alternatives are derived, and the relationship with tests for corresponding moving average unit roots is explored. We also propose nonparametric modifications of these test statistics designed to have limit distributions which are free of nuisance parameters under weaker conditions on the errors. Our tests are shown to contain existing stationarity tests as special cases and to extend these tests in a number of useful directions.
UR - http://www.scopus.com/inward/record.url?scp=0142230490&partnerID=8YFLogxK
U2 - 10.1111/1467-9892.00324
DO - 10.1111/1467-9892.00324
M3 - Article
SN - 1467-9892
SN - 1467-9892
SN - 1467-9892
VL - 24
SP - 591
EP - 612
JO - Journal of Time Series Analysis
JF - Journal of Time Series Analysis
ER -