Testing for strict stationarity in a random coefficient autoregressive model

Trapani, Lorenzo

Abstract

We propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of non-stationarity, in the context of a Random Coefficient AutoRegression (RCAR). The procedure is based on randomising a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative. Thence, we propose a randomised test which can be used directly and-building on it-a decision rule to discern between the null and the alternative. The procedure can be applied under very general circumstances: albeit developed for an RCAR model, it can be used in the case of a standard AR(1) model, without requiring any modifications or prior knowledge. Also, the test works (again with no modification or prior knowledge being required) in the presence of infinite variance, and in general requires minimal assumptions on the existence of moments.

Citation

Trapani, L. (2021). Testing for strict stationarity in a random coefficient autoregressive model. Econometric Reviews, 40(3), 220-256. https://doi.org/10.1080/07474938.2020.1773667

• Journal Article Type: Article
• Acceptance Date: May 19, 2020
• Online Publication Date: Jun 12, 2020
• Publication Date: 2021
• Deposit Date: May 21, 2020
• Publicly Available Date: Jun 13, 2021
• Journal: Econometric Reviews
• Print ISSN: 0747-4938
• Electronic ISSN: 1532-4168
• Publisher: Taylor & Francis Open
• Peer Reviewed: Peer Reviewed
• Volume: 40
• Issue: 3
• Pages: 220-256
• DOI: https://doi.org/10.1080/07474938.2020.1773667
• Keywords: Random Coefficient AutoRegression; Stationarity; Unit Root; Heavy Tails; Ran- domised Tests AMS 2000 subject classification: Primary 62F05; secondary 62M10
• Public URL: https://nottingham-repository.worktribe.com/output/4481414
• Publisher URL: https://www.tandfonline.com/doi/full/10.1080/07474938.2020.1773667
• Additional Information: This is an Accepted Manuscript of an article published by Taylor & Francis in Econometric Reviews on 12 June 2020, available online: http://www.tandfonline.com/10.1080/07474938.2020.1773667