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.

中文翻译：

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在随机系数自回归模型中检验严格平稳性

我们提出了一个程序，在随机系数自回归 (RCAR) 的背景下，在（严格）平稳性的零假设和非平稳性的替代方案之间做出决定。该过程基于随机化诊断，该诊断在零值下发散到正无穷大，在替代下漂移到零。因此，我们提出了一个可以直接使用的随机测试，并在此基础上建立了一个决策规则来区分无效和替代。该过程可以在非常普遍的情况下应用：尽管它是为 RCAR 模型开发的，但它可以用于标准 AR(1) 模型的情况，无需任何修改或先验知识。此外，测试在存在无限方差的情况下工作（同样不需要修改或先验知识），