Asymptotic inference for a sign-double autoregressive (SDAR) model of order one

We propose an extension of the double autoregressive (DAR) model: the sign-double autoregressive (SDAR) model, in the spirit of the GJR-GARCH model (also named the sign-ARCH model). Our model shares the important property of DAR models where a unit root does not imply non stationarity and it allows for asymmetry, as other alternatives in the literature such as the GJR-GARCH or asymmetric linear DAR and dual-asymmetry linear DAR models. We establish consistency and asymptotic normality of the quasi-maximum likelihood estimator in the context of the SDAR model. Furthermore, it is shown by simulations that the asymptotic properties also apply in finite samples. Finally, an empirical application shows the usefulness of our model specially in periods of supply/demand crises of oil disruptions, where spikes of volatility are very likely to be predominant.

本文提出双自回归模型（double autoregressive, DAR）的一种扩展形式——符号双自回归模型（sign-double autoregressive, SDAR），其设计灵感源自GJR-GARCH模型（亦称符号ARCH模型）。本模型保留了DAR模型的核心特性：单位根并不意味着非平稳性，同时支持不对称性设定，与现有文献中的GJR-GARCH、不对称线性DAR以及双不对称线性DAR等同类模型具备一致的重要属性。本文推导了SDAR模型框架下拟极大似然估计量的一致性与渐近正态性。进一步通过模拟实验证实，该渐近性质在有限样本场景下同样适用。最后一项实证应用表明，本文所提模型在石油供应/需求中断危机时期尤为实用，这类时期内波动率尖峰往往占据主导地位。