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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)


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.

Suggested Citation

  • Violetta Dalla & Liudas Giraitis & Peter C.B. Phillips, 2015. "Testing Mean Stability of Heteroskedastic Time Series," Working Papers 765, Queen Mary University of London, School of Economics and Finance.
  • Handle: RePEc:qmw:qmwecw:wp765

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    More about this item


    Heteroskedasticity; KPSS test; Mean stability; Variance stability; VS test;

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C23 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Models with Panel Data; Spatio-temporal Models

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