Time series models are often ﬁtted to the data without preliminary checks for stability of the mean and variance, conditions that may not hold in much economic and ﬁnancial data, particularly over long periods. Ignoring such shifts may result in ﬁtting models with spurious dynamics that lead to unsupported and controversial conclusions about time dependence, causality, and the eﬀects of unanticipated shocks. In spite of what may seem as obvious diﬀerences between a time series of independent variates with changing variance and a stationary conditionally heteroskedastic (GARCH) process, such processes may be hard to distinguish in applied work using basic time series diagnostic tools. We develop and study some practical and easily implemented statistical procedures to test the mean and variance stability of uncorrelated and serially dependent time series. Application of the new methods to analyze the volatility properties of stock market returns leads to some unexpected surprising ﬁndings concerning the advantages of modeling time varying changes in unconditional variance.
Dalla, Violetta; Giraitis, Liudas; and Phillips, Peter C.B., "Testing Mean Stability of Heteroskedastic Time Series" (2015). Cowles Foundation Discussion Papers. 2441.