Inference on a Structural Break in Trend with Fractionally Integrated Errors

Seong Yeon Chang and Pierre Perron

No wp2015-011, Boston University - Department of Economics - Working Papers Series from Boston University - Department of Economics

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.

Keywords: Fractionally integrated process; Linear trend; Segmented trend; Spurious break; Structural change (search for similar items in EconPapers)
JEL-codes: C13 C18 C22 (search for similar items in EconPapers)
Date: 2014-04-30, Revised 2015-09-20
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Related works:
Journal Article: Inference on a Structural Break in Trend with Fractionally Integrated Errors (2016)
Working Paper: Inference on a Structural Break in Trend with Fractionally Integrated Errors (2013)
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