This paper obtains the joint limiting distribution of residuals and squared residuals of a general time-series model. Based on this, we propose a mixed portmanteau statistic for testing the adequacy of fitted time-series models. In some cases, it is shown that this statistic can be simply...

This paper investigates regression quantiles (RQ) for unstable autoregressive models. The uniform Bahadur representation of the RQ process is obtained. The joint asymptotic distribution of the RQ process is derived in a unified manner for all types of characteristic roots on or outside the unit...

The paper considers the double-autoregressive model "y"_"t" &equals; "φ""y"_{"t" - 1}&plus;"&epsiv;"_"t" with "&epsiv;"_"t" &equals;<formula format="inline"><file name="rssb_432_mu1.gif" type="gif" /></formula>. Consistency and asymptotic normality of the estimated parameters are proved under the condition "E" ln |"φ" &plus;√"&agr;""η"_{"t"</ sub>|0, which includes the cases with |"φ"|&equals;1 or |"φ"|1 as well...<//>}

Least squares (LS) and maximum likelihood (ML) estimation are considered for unit root processes with GARCH (1, 1) errors. The asymptotic distributions of LS and ML estimators are derived under the condition α + β  1. The former has the usual unit root distribution and the latter is a...