Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models

Horváth, Lajos; Trapani, Lorenzo

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. (2023). Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models. Journal of Business and Economic Statistics, 41(4), 1300-1314. https://doi.org/10.1080/07350015.2022.2120485

• Journal Article Type: Article
• Acceptance Date: Aug 25, 2022
• Online Publication Date: Oct 11, 2022
• Publication Date: Oct 2, 2023
• Deposit Date: Aug 30, 2022
• Publicly Available Date: Oct 12, 2023
• Journal: Journal of Business and Economic Statistics
• Print ISSN: 0735-0015
• Electronic ISSN: 1537-2707
• Publisher: Informa UK Limited
• Peer Reviewed: Peer Reviewed
• Volume: 41
• Issue: 4
• Pages: 1300-1314
• DOI: https://doi.org/10.1080/07350015.2022.2120485
• Keywords: Changepoint problem; Heteroscedasticity; Nonstationarity; Random coefficient autoRegression; Weighted CUSUM process
• Public URL: https://nottingham-repository.worktribe.com/output/10630761
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/07350015.2022.2120485