Robust Stationarity Tests in Seasonal Time Series Processes
针对季节性时间序列中部分频率存在未处理单位根时，传统平稳性检验失效的问题，提出基于数据预滤波的修正方法，并通过蒙特卡洛模拟和英国消费支出数据验证其有效性。
This article builds on the existing literature on (stationarity) tests of the null hypothesis of deterministic seasonality in a univariate time series process against the alternative of unit root behavior at some or all of the zero and seasonal frequencies. This article considers the case where, in testing for unit roots at some proper subset of the zero and seasonal frequencies, there are unattended unit roots among the remaining frequencies. Monte Carlo results are presented that demonstrate that in this case, the stationarity tests tend to distort below nominal size under the null and display an associated (often very large) loss of power under the alternative. A modification to the existing tests, based on data prefiltering, that eliminates the problem asymptotically is suggested. Monte Carlo evidence suggests that this procedure works well in practice, even at relatively small sample sizes. Applications of the robustified statistics to various seasonally unadjusted time series measures of U.K. consumers' expenditure are considered; these yield considerably more evidence of seasonal unit roots than do the existing stationarity tests.