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A linear regression model with persistent level shifts: An alternative to infill asymptotics

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  • Woody, Jonathan
  • Lund, Robert

Abstract

A changepoint in a time series is a time of change in the marginal distribution, autocovariance, or any other distributional structure of the series. Examples include mean level shifts and volatility (variance) changes. Climate data, for example, is replete with mean shift changepoints, occurring whenever a recording instrument is changed or the observing station is moved. Here, we consider the problem of incorporating known changepoint times into a regression model framework. Specifically, we establish consistency and asymptotic normality of ordinary least squares regression estimators that account for an arbitrary number of mean shifts in the record. In a sense, this provides an alternative to the customary infill asymptotics for regression models that assume an asymptotic infinity of data observations between all changepoint times.

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  • 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.
    • Handle: RePEc:eee:stapro:v:95:y:2014:i:c:p:118-124
    DOI: 10.1016/j.spl.2014.08.018
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    References listed on IDEAS

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    1. Jushan, Bai, 1995. "Estimation of multiple-regime regressions with least absolutes deviation," MPRA Paper 32916, University Library of Munich, Germany, revised Feb 1998.
    2. Alexander Aue & Lajos Horváth, 2013. "Structural breaks in time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 34(1), pages 1-16, January.
    3. 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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    1. Woody, Jonathan, 2015. "Time series regression with persistent level shifts," Statistics & Probability Letters, Elsevier, vol. 102(C), pages 22-29.

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