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Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models

Horváth, Lajos; Trapani, Lorenzo

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Lajos Horváth

Lorenzo Trapani


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.


Horváth, L., & Trapani, L. (2023). Changepoint Detection in Heteroscedastic Random Coefficient Autoregressive Models. Journal of Business and Economic Statistics, 41(4), 1300-1314.

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
Keywords Changepoint problem; Heteroscedasticity; Nonstationarity; Random coefficient autoRegression; Weighted CUSUM process
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