Inference on a Structural Break in Trend with Fractionally Integrated Errors

Abstract

Perron and Zhu (2005) established the consistency, convergence rate and limiting distributions of parameter estimates in time trends with a change in slope with or without a concurrent level change for the cases with I(1) or I(0) errors. We extend their analysis to the general case of fractionally integrated errors with memory parameter d∗. Our results uncover interesting features; e.g., with a level shift allowed, the convergence rate for the break date estimate is the same for all d∗∈(−0.5,0.5). In other cases, it is decreasing as d∗ increases. We also provide results about the so‐called spurious break issue.

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