Test for Change in Error Variance of Multiple Time Series

Changes in levels of multiple time series based on their common components helps characterize the shared behavior of the data generating process with known events causing perturbations in their movements. However, changes in variance of the error structure leads to misspecification of models that complicates statistical inference. Volatility structures may incorporate variance into the time series models, but these can easily lead to overparameterization in multiple time series. A model with inherent changes in variance structure is used to develop a bootstrap-based test for presence of changes in variance of multiple time series. Simulation studies shows that the test is correctly-sized and powerful compared to CUSUM-based test in a wide range of scenarios. The test is advantageous specially in the presence of strong autocorrelations and even in unbalanced data. Using global stock prices with the onset of lockdowns against the COVID19 pandemic as the stimulus of the changepoint, the test was able to detect significant changes in error variance before and during the pandemic. While CUSUM-based test also recognized the significant changes in multiple time series, linear trend was misconstrued as evidence of the presence of change in variance in stock prices.