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Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models

Horváth, Lajos; Trapani, Lorenzo

Authors

Lajos Horváth

Lorenzo Trapani



Abstract

We propose a family of CUSUM-based statistics to detect the presence of changepoints in the deterministic part of the autoregressive parameter in a Random Coefficient Autoregressive (RCA) sequence. Our tests can be applied irrespective of whether the sequence is stationary or not, and no prior knowledge of stationarity or lack thereof is required. Similarly, our tests can be applied even when the error term and the stochastic part of the autoregressive coefficient are non iid, covering the cases of conditional volatility and shifts in the variance, again without requiring any prior knowledge as to the presence or type thereof. In order to ensure the ability to detect breaks at sample endpoints, we propose weighted CUSUM statistics, deriving the asymptotics for virtually all possible weighing schemes, including the standardized CUSUM process (for which we derive a Darling-Erdős theorem) and even heavier weights (so-called Rényi statistics). Simulations show that our procedures work very well in finite samples. We complement our theory with an application to several financial time series.

Citation

Horváth, L., & Trapani, L. (2022). Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models. Journal of Business and Economic Statistics, https://doi.org/10.1080/07350015.2022.2120485

Journal Article Type Article
Acceptance Date Aug 25, 2022
Online Publication Date Sep 7, 2022
Publication Date Sep 7, 2022
Deposit Date Aug 30, 2022
Publicly Available Date Sep 8, 2023
Journal Journal of Business and Economic Statistics
Print ISSN 0735-0015
Electronic ISSN 1537-2707
Publisher Taylor and Francis
Peer Reviewed Peer Reviewed
DOI https://doi.org/10.1080/07350015.2022.2120485
Keywords Statistics, Probability and Uncertainty; Economics and Econometrics; Social Sciences (miscellaneous); Statistics and Probability
Public URL https://nottingham-repository.worktribe.com/output/10630761
Publisher URL https://www.tandfonline.com/doi/full/10.1080/07350015.2022.2120485