On dual-asymmetry linear double AR models

This paper introduces a dual-asymmetry linear double autoregressive (DA-LDAR) model that can allow for asymmetric eﬀects in both the conditional location and volatility components of time series data. The strict stationarity is discussed for the new model, for which a suﬃcient condition is established. A self-weighted exponential quasi-maximum likelihood estimator (EQMLE) is proposed for the DA-LDAR model, and a mixed portmanteau test for goodness-of-ﬁt is constructed based on the self-weighted EQMLE. It is noteworthy that all the asymptotic properties for estimation and testing are established without any moment condition on the data process, which makes the new model and its inference tools applicable for heavy-tailed data. Since all inference tools need to estimate the unknown density function of innovations, we employ a random-weighting bootstrap method to facilitate accurate inference and show its asymptotic validity. Simulation studies provide support for theoretical results, and an empirical application to NASDAQ Composite Index illustrates the usefulness of the new model.