On vector linear double autoregression

Abstract

This article proposes a vector linear double autoregressive (VLDAR) model with the constant conditional correlation specification, which can capture the co‐movement of multiple series and jointly model their conditional means and volatilities. The strict stationarity of the new model is discussed, and a self‐weighted Gaussian quasi‐maximum likelihood estimator (SQMLE) is proposed for estimation. To reduce the computational cost, especially when the series dimension is large, a block coordinate descent (BCD) algorithm is provided to calculate the SQMLE. Moreover, a Bayesian information criterion is introduced for order selection, and a multi‐variate mixed portmanteau test is constructed for checking the adequacy of fitted models. All asymptotic properties for estimation, model selection, and portmanteau test are established without any moment restrictions imposed on the data process, which makes the new model and its inference tools applicable for heavy‐tailed data. Simulation experiments are conducted to evaluate the finite‐sample performance of the proposed methodology, and an empirical example on analyzing S&P 500 sector indices is presented to illustrate the usefulness of the new model in contrast with competitors.