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No. 765: Testing Mean Stability of Heteroskedastic Time Series

Violetta Dalla , National and Kapodistrian University of Athens
Liudas Giraitis , Queen Mary University of London
Peter C.B. Phillips , Yale University, University of Auckland, University of Southampton, Singapore Management University

December 18, 2015

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Abstract

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.

J.E.L classification codes: C22, C23

Keywords:Heteroskedasticity, KPSS test, Mean stability, Variance stability, VS test

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