Abstract

The purpose of this study is to investigate the effects of temporal aggregation on modeling and testing a single variance-change in a univariate time series process. We show that the aggregation effect on the variance-change ARMA model can be explained only with non-aggregate model parameters, based on functional links between a non-aggregate process and its m-aggregate process. In addition, through Monte Carlo simulations and a real data example, we compare empirical powers for the two CUSUMSQ tests—Lee and Park’s test and Inclán and Tiao’s test under given conditions of temporal aggregation and find out a better performance on the Inclán and Tiao CUSUMSQ test at moderate-level aggregation despite severe information loss on both tests at high-level aggregation.

摘要

本研究的目的是研究时间聚合对单变量时间序列过程中单个方差变化建模和测试的影响。我们证明，基于非聚合过程与其 m聚合过程之间的功能链接，只能用非聚合模型参数来解释方差变化 ARMA 模型的聚合效应。此外，通过蒙特卡罗模拟和真实数据示例，我们比较了两种 CUSUMSQ 测试（Lee 和 Park 的测试以及 Inclán 和 Tiao 的测试）在给定时间聚合条件下的经验功效，并发现 Inclán 和 Tiao CUSUMSQ 测试在中等级别聚合时具有更好的性能，尽管这两种测试在高级聚合时都存在严重的信息丢失。