Uniform convergence of sample second moments of families of time series arrays

• 成果类型: Article
• 署名作者: Findley, DF; Pötscher, BM; Wei, CZ
• 署名单位: University of Vienna; Academia Sinica - Taiwan
• 刊物名称: ANNALS OF STATISTICS
• ISSN/ISSBN: 0090-5364
• 发表日期: 2001
• 页码: 815-838
• 关键词: seasonal-adjustment; MODEL

摘要

We consider abstractly defined time series arrays y(t)(T), 1 less than or equal to t less than or equal to T, requiring only that their sample lagged second moments converge and that their end values y(1+j)(T) and y(T-j)(T) be of order less than T-1/2 for each j greater than or equal to 0. We show that, under quite general assumptions, various types of arrays that arise naturally in time series analysis have these properties, including regression residuals from a time series regression, seasonal adjustments and infinite variance processes rescaled by their sample standard deviation. We establish a useful uniform convergence result, namely that these properties are preserved in a uniform way when relatively compact sets of absolutely summable filters are applied to the arrays. This result serves as the foundation for the proof, in a companion paper by Findley, Potscher and Wei, of the consistency of parameter estimates specified to minimize the sample mean squared multistep-ahead forecast error when invertible short-memory models are fit to (short- or long-memory) time series or time series arrays.