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Inference on a Structural Break in Trend with Fractionally Integrated Errors

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  • Seong Yeon Chang
  • Pierre Perron

Abstract

Perron and Zhu (2005) established the consistency, rate of convergence and the limiting distributions of parameter estimates in a linear time trend with a change in slope with or without a concurrent change in level. They considered the dichotomous cases whereby the errors are shortmemory stationary, I(0), or have an autoregressive unit root, I(1). We extend their analysis to cover the more general case of fractionally integrated errors for values of d in the interval (0:5, 1:5) excluding the boundary case 0:5. Our theoretical results uncover some interesting features. For example, when a concurrent level shift is allowed, the rate of convergence of the estimate of the break date is the same for all values of d in the interval (0:5;0:5). This feature is linked to the contamination induced by allowing a level shift, previously discussed by Perron and Zhu (2005). In all other cases, the rate of convergence is monotonically decreasing as d increases. We also provide results about the so-called spurious break issue. Simulation experiments are provided to illustrate some of the theoretical results.
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  • Seong Yeon Chang & Pierre Perron, 2016. "Inference on a Structural Break in Trend with Fractionally Integrated Errors," Journal of Time Series Analysis, Wiley Blackwell, vol. 37(4), pages 555-574, July.
  • Handle: RePEc:bla:jtsera:v:37:y:2016:i:4:p:555-574
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    File URL: http://hdl.handle.net/10.1111/jtsa.12176
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    Cited by:

    1. Zongwu Cai & Seong Yeon Chang, 2018. "A New Test In A Predictive Regression with Structural Breaks," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 201811, University of Kansas, Department of Economics, revised Dec 2018.
    2. Pierre Perron, 2017. "Unit Roots and Structural Breaks," Econometrics, MDPI, Open Access Journal, vol. 5(2), pages 1-3, May.
    3. Wenger, Kai & Leschinski, Christian & Sibbertsen, Philipp, 2018. "A simple test on structural change in long-memory time series," Economics Letters, Elsevier, vol. 163(C), pages 90-94.
    4. Alessandro Casini & Pierre Perron, 2018. "Structural Breaks in Time Series," Papers 1805.03807, arXiv.org.
    5. Seong Yeon Chang & Pierre Perron, 2017. "Fractional Unit Root Tests Allowing for a Structural Change in Trend under Both the Null and Alternative Hypotheses," Econometrics, MDPI, Open Access Journal, vol. 5(1), pages 1-26, January.

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    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C18 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Methodolical Issues: General
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes

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