Alessandro Casini, Pierre Perron
arXiv 3 Jun 2021 · Mathematics — Statistics Theory · publishedJournal of Econometrics (2024) · 9 citations (OpenAlex)
arXiv:2106.02031 · PDF · DOI · OpenAlex · Extracted main text
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. Our method can be used across many fields and a companion program is made available in popular software packages.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Last, M., Shumway, R (2008) Detecting abrupt changes in a piecewise locally stationary time series | 1.000 | 7 | 3 | 100% |
| 2 | Casini, A (2023) Theory of evolutionary spectra for heteroskedasticity and autocorrelation robust inference in possibly misspecified and nonstati… self | 0.961 | 9 | 5 | 89% |
| 3 | Nakamura, E., Steinsson, J (2018) High frequency identification of monetary non-neutrality: The information effect | 0.874 | 5 | 2 | 100% |
| 4 | Ingster, Y.I (1993) Asymptotically minimax hypothesis testing for nonparametric alternatives I, II, III | 0.843 | 3 | 3 | 100% |
| 5 | Bibinger, M., Jirak, M., Vetter, M (2017) Nonparametric change-point analysis of volatility | 0.814 | 13 | 5 | 54% |
| 6 | Dahlhaus, R (1997) Fitting time series models to nonstationary processes | 0.794 | 8 | 3 | 50% |
| 7 | Wu, W.B., Zhao, Z (2007) Inference of trends in time series | 0.737 | 4 | 3 | 50% |
| 8 | Wu, W.B., Zhou, Z (2011) Gaussian approximation for non-stationary multiple time series | 0.737 | 4 | 2 | 75% |
| 9 | Wu, W.B (2007) Strong invariance principles for dependent random variables | 0.737 | 4 | 2 | 75% |
| 10 | Yao, Y (1987) Approximating the distribution of the ML estimate of the change-point in a sequence of independent random variables | 0.737 | 3 | 2 | 100% |
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