## Statistics Colloquium, Dr. Bu Hyoung Lee

#### Department of Mathematics and Statistics, Loyola University

**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.