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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 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.

Suggested Citation

  • Lorenzo Trapani, 2018. "Testing for strict stationarity in a random coefficient autoregressive model," Discussion Papers 18/02, University of Nottingham, Granger Centre for Time Series Econometrics.
    • Handle: RePEc:not:notgts:18/02
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    4. 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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    Keywords

    Random Coefficient AutoRegression; Stationarity; Unit Root; Heavy Tails; Randomised Tests.;
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