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Change-point analysis of time series with evolutionary spectra

Alessandro Casini and Pierre Perron

Journal of Econometrics, 2024, vol. 242, issue 2

Abstract: This paper develops change-point methods for the spectrum of a locally stationary time series. We focus on series with a bounded spectral density that change smoothly under the null hypothesis but exhibits change-points or becomes less smooth under the alternative. We address two local problems. The first is the detection of discontinuities (or breaks) in the spectrum at unknown dates and frequencies. The second involves abrupt yet continuous changes in the spectrum over a short time period at an unknown frequency without signifying a break. Both problems can be cast into changes in the degree of smoothness of the spectral density over time. We consider estimation and minimax-optimal testing. We determine the optimal rate for the minimax distinguishable boundary, i.e., the minimum break magnitude such that we are able to uniformly control type I and type II errors. We propose a novel procedure for the estimation of the change-points based on a wild sequential top-down algorithm and show its consistency under shrinking shifts and possibly growing number of change-points.

Keywords: Change-point; Locally stationary; Frequency domain; Minimax-optimal test (search for similar items in EconPapers)
JEL-codes: C12 C13 C22 (search for similar items in EconPapers)
Date: 2024
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Working Paper: Change-Point Analysis of Time Series with Evolutionary Spectra (2024) Downloads
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Persistent link: https://EconPapers.repec.org/RePEc:eee:econom:v:242:y:2024:i:2:s030440762400157x

DOI: 10.1016/j.jeconom.2024.105811

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Journal of Econometrics is currently edited by T. Amemiya, A. R. Gallant, J. F. Geweke, C. Hsiao and P. M. Robinson

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