We develop tests for the presence of deterministic seasonal behaviour and seasonal mean shifts in a seasonally observed univariate time series. These tests are designed to be asymptotically robust to the order of integration of the series at both the zero and seasonal frequencies. Motivated by the approach of Hylleberg, Engle, Granger and Yoo [1990, Journal of Econometrics vol. 44, pp. 215-238], we base our approach on linear filters of the data which remove any potential unit roots at the frequencies not associated with the deterministic component(s) under test. Test statistics are constructed using the filtered data such that they have well defined limiting null distributions regardless of whether the data are either integrated or stationary at the frequency associated with the deterministic component(s) under test. In the same manner as Vogelsang [1998, Econometrica vol. 66, pp. 123-148], Bunzel and Vogelsang [2005, Journal of Business and Economic Statistics vol. 23, pp. 381-394] and Sayginsoy and Vogelsang [2011, Econometric Theory vol. 27, pp. 992-1025], we scale these statistics by a function of an auxiliary seasonal unit root statistic. This allows us to construct tests which are asymptotically robust to the order of integration of the data at both the zero and seasonal frequencies. Monte Carlo evidence suggests that our proposed tests have good finite sample size and power properties. An empirical application to U.K. GDP indicates the presence of seasonal mean shifts in the data.

中文翻译：

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确定性季节性和季节性均值变化的稳健检验1

我们针对在季节性观察到的单变量时间序列中确定性的季节性行为和季节性均值漂移的存在进行测试。这些测试被设计为在零频率和季节性频率上对序列的积分顺序渐近鲁棒。受Hylleberg，Engle，Granger和Yoo [1990年，计量经济学杂志》第1卷的影响。[44]，第215-238页]，我们的方法基于数​​据的线性滤波器，该线性滤波器以与被测确定性分量无关的频率去除任何潜在的单位根。使用过滤后的数据构建测试统计数据，以使它们具有定义明确的限制零分布，而无论数据是在与待测确定性组件相关联的频率下是完整的还是固定的。以与Vogelsang [1998，Econometrica vol。66，第123-148页]，Bunzel和Vogelsang [2005年，《商业与经济统计杂志》第1卷。23，第381-394页]，Sayginsoy和Vogelsang [2011年，计量经济学理论》，第23卷。27，pp。992-1025]，我们通过辅助季节性单位根统计量的函数来缩放这些统计量。这使我们能够构建对零频率和季节性频率的数据积分顺序渐近鲁棒的测试。蒙特卡洛证据表明，我们提出的测试具有良好的有限样本量和功效特性。对英国GDP的经验应用表明数据中存在季节性均值漂移。计量经济学理论卷 27，pp。992-1025]，我们通过辅助季节性单位根统计量的函数来缩放这些统计量。这使我们能够构建对零频率和季节性频率的数据积分顺序渐近鲁棒的测试。蒙特卡洛证据表明，我们提出的测试具有良好的有限样本量和功效特性。对英国GDP的经验应用表明数据中存在季节性均值漂移。计量经济学理论卷 27，pp。992-1025]，我们通过辅助季节性单位根统计量的函数来缩放这些统计量。这使我们能够构建对零频率和季节性频率的数据积分顺序渐近鲁棒的测试。蒙特卡洛证据表明，我们提出的测试具有良好的有限样本量和功效特性。对英国GDP的经验应用表明数据中存在季节性均值漂移。