Title: The Use of Temporally Aggregated Data in Testing for a Variance Change in a Time Series
Abstract: In this research, we investigate the effects of temporal aggregation on the cumulative sum of squares (CUSUMSQ) test for a variance change in a time series. First, we derive the exact parameters of an aggregate ARIMA model from the structural relationship between non-aggregated and aggregated processes. Using those results, we propose a modified CUSUMSQ test for a variance change in an aggregate series. Then, we find the null distribution of the modified test for every aggregation. Through Monte Carlo simulations, we show that the empirical null distribution moves right and so the statistical power of the test decreases as temporal aggregation intensifies. That is, the test results are influenced by the aggregation which causes the loss of information about the variance of a time series process. Also, we illustrate the aggregation effects on the test procedure through the two real data.