This paper studies the self-weighted least squares estimator (SWLSE) of the ARMA model with GARCH noises. It is shown that the SWLSE is consistent and asymptotically normal when the GARCH noise does not have a finite fourth moment. Using the residuals from the estimated ARMA model, it is shown...

This paper studies the self-weighted least squares estimator (SWLSE) of the ARMA model with GARCH noises. It is shown that the SWLSE is consistent and asymptotically normal when the GARCH noise does not have a finite fourth moment. Using the residuals from the estimated ARMA model, it is shown...

This paper first derives the limiting distributions of the residual and the squared residual autocorrelation functions of the nonstationary autoregressive moving-average model, respectively. We then use them to construct two portmanteau statistics for testing the adequacy of the fitted model....

This paper investigates the global self-weighted least absolute deviation (SLAD) estimator for finite and infinite variance ARMA(<italic>p</italic>, <italic>q</italic>) models. The strong consistency and asymptotic normality of the global SLAD estimator are obtained. A simulation study is carried out to assess the performance of...