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Time series regression with persistent level shifts

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  • Woody, Jonathan

Abstract

A changepoint in a time series is a time in which any change in the distributional form (marginal or joint) of the series occurs. This includes changes in mean or covariance structure of the time series. Mean level shift changepoints have been shown to dramatically influence linear trend estimates obtained from a simple linear regression model. This study provides an asymptotic analysis of a time series regression model experiencing an increasing number of mean level shifts at known times. It is shown that one may consistently estimate any finite number of unknown parameters in a time series polynomial regression, so long as two or more consecutive observations without a changepoint occurs infinity often in the limit.

Suggested Citation

  • Woody, Jonathan, 2015. "Time series regression with persistent level shifts," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 22-29.
    • Handle: RePEc:eee:stapro:v:102:y:2015:i:c:p:22-29
    DOI: 10.1016/j.spl.2015.03.011
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    References listed on IDEAS

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    1. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    2. Jushan Bai & Pierre Perron, 1998. "Estimating and Testing Linear Models with Multiple Structural Changes," Econometrica, Econometric Society, vol. 66(1), pages 47-78, January.
    3. Aue, Alexander & Gabrys, Robertas & Horváth, Lajos & Kokoszka, Piotr, 2009. "Estimation of a change-point in the mean function of functional data," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2254-2269, November.
    4. Roussas, George G., 1989. "Consistent regression estimation with fixed design points under dependence conditions," Statistics & Probability Letters, Elsevier, vol. 8(1), pages 41-50, May.
    5. Woody, Jonathan & Lund, Robert, 2014. "A linear regression model with persistent level shifts: An alternative to infill asymptotics," Statistics & Probability Letters, Elsevier, vol. 95(C), pages 118-124.
    6. Venkata Jandhyala & Stergios Fotopoulos & Ian MacNeill & Pengyu Liu, 2013. "Inference for single and multiple change-points in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(4), pages 423-446, July.
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