This paper considers adaptive estimation in nonstationary autoregressive moving average models with the noise sequence satisfying a generalised autoregressive conditional heteroscedastic process. The locally asymptotic quadratic form of the log-likelihood ratio for the model is obtained. It is...

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...