Temporal Aggregation Effects on Testing for a Variance Change of a Time Series

• Activity Number: 489
• Type: Contributed
• Date/Time: Wednesday, August 12, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Business and Economic Statistics Section
• Author(s): Bu Hyoung Lee* and William W.S. Wei
• Companies: Temple University and Temple University
• Keywords: Temporal Aggregation ; Model Transformation ; Variance Change ; Cumulative Sum of Squares Test

Abstract

We investigate the effects of temporal aggregation on the cumulative sum of squares (CUSUMSQ) test to detect a variance change in a time series. First, we derive the proper parameter transformation of an aggregate ARIMA model. When temporally aggregated data are used, we show that two aggregation quantities, which are from the aggregate model parameters, in the CUSUMSQ test statistic have effects on test results. Then, we propose a modified CUSUMSQ test to control the aggregation effects. Through Monte Carlo simulations, the modified CUSUMSQ test shows better performance and higher test powers to detect a variance change in an aggregated time series.