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.