Signal extraction goodness-of-fit diagnostic tests under model parameter uncertainty: Formulations and empirical evaluation
提出一种基于信号提取方差的时域拟合优度诊断检验，修正了模型参数不确定性导致的统计量偏小问题，适用于非平稳时间序列，并通过蒙特卡洛研究和美国人口普查局数据验证其有效性，可作为季节调整从业者的辅助模型检验工具。
We present a time-domain goodness-of-fit (gof) diagnostic test that is based on signal-extraction variances for nonstationary time series. This diagnostic test extends the time-domain gof statistic of Maravall (2003 Maravall, A. (2003). A class of diagnostics in the ARIMA-model-based decomposition of a time series. Memorandum, Bank of Spain. Available at http://www.bde.es/servicio/software/tramo/diagnosticsamb.pdf [Google Scholar]) by taking into account the effects of model parameter uncertainty, utilizing theoretical results of McElroy and Holan (2009 McElroy, T., Holan, S. (2009). A local spectral approach for assessing time series model misspecification. Journal of Multivariate Analysis 100:604–621.[Crossref], [Web of Science ®] , [Google Scholar]). We demonstrate that omitting this correction results in a severely undersized statistic. Adequate size and power are obtained in Monte Carlo studies for fairly short time series (10 to 15 years of monthly data). Our Monte Carlo studies of finite sample size and power consider different combinations of both signal and noise components using seasonal, trend, and irregular component models obtained via canonical decomposition. Details of the implementation appropriate for SARIMA models are given. We apply the gof diagnostic test statistics to several U.S. Census Bureau time series. The results generally corroborate the output of the automatic model selection procedure of the X-12-ARIMA software, which in contrast to our diagnostic test statistic does not involve hypothesis testing. We conclude that these diagnostic test statistics are a useful supplementary model-checking tool for practitioners engaged in the task of model-based seasonal adjustment.