We propose a near-explosive random coefficient autoregressive model (NERC) to obtain predictive probabilities of the apparition and devolution of bubbles. The distribution of the autoregressive coefficient of this model is allowed to be centred at an O(T^−α) distance of unity, with α ∈ (0, 1). When the expectation of the autoregressive coefficient lies on the explosive side of unity, the NERC helps to model the temporary explosiveness of time series and obtain related predictive probabilities. We study the asymptotic properties of the NERC and provide a procedure for inference on the parameters. In empirical illustrations, we estimate predictive probabilities of bubbles or flash crashes in financial asset prices.

中文翻译：

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气泡和闪光崩溃的概率预测

我们提出了一种近爆随机系数自回归模型（NERC），以获得气泡的出现和散发的预测概率。该模型的自回归系数的分布以a （∈（0，1））的O（T- ^α）距离为中心。当自回归系数的期望值位于统一的爆炸性一侧时，NERC有助于对时间序列的临时爆炸性进行建模，并获得相关的预测概率。我们研究了NERC的渐近性质，并提供了一个推断参数的程序。在经验例证中，我们估计金融资产价格中泡沫或闪崩的预测概率。