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Testing for strict stationarity in a random coefficient autoregressive model

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  • Lorenzo Trapani

Abstract

We propose a procedure to decide between the null hypothesis of (strict) stationarity and the alternative of nonstationarity, in the context of a random coefficient autoregression (RCAR). The procedure is based on randomizing a diagnostic which diverges to positive infinity under the null, and drifts to zero under the alternative. Thence, we propose a randomized 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.

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  • Lorenzo Trapani, 2021. "Testing for strict stationarity in a random coefficient autoregressive model," Econometric Reviews, Taylor & Francis Journals, vol. 40(3), pages 220-256, April.
    • Handle: RePEc:taf:emetrv:v:40:y:2021:i:3:p:220-256
    DOI: 10.1080/07474938.2020.1773667
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    2. Marie Badreau & Frédéric Proïa, 2023. "Consistency and asymptotic normality in a class of nearly unstable processes," Statistical Inference for Stochastic Processes, Springer, vol. 26(3), pages 619-641, October.
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    4. Aknouche, Abdelhakim & Gouveia, Sonia & Scotto, Manuel, 2023. "Random multiplication versus random sum: auto-regressive-like models with integer-valued random inputs," MPRA Paper 119518, University Library of Munich, Germany, revised 18 Dec 2023.
    5. Trapani, Lorenzo, 2021. "A test for strict stationarity in a random coefficient autoregressive model of order 1," Statistics & Probability Letters, Elsevier, vol. 177(C).

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