QMLE OF PERIODIC BILINEAR MODELS AND OF PARMA MODELS WITH PERIODIC BILINEAR INNOVATIONS

This paper develops an asymptotic inference theory for bilinear (BL) time series models with periodic coefficients (PBL for short). For this purpose, we establish firstly a necessary and sufficient conditions for such models to have a unique stationary and ergodic solutions (in periodic sense). Secondly, we examine the consistency and the asymptotic normality of the quasi-maximum likelihood estimator (QMLE) under very mild moment condition for the innovation errors. As a result, it is shown that whenever the model is strictly stationary, the moment of some positive order of PBL model exists and is finite, under which the strong consistency and asymptotic normality of QMLE for PBL are proved. Moreover, we consider also the periodic ARMA (PARMA) models with PBL innovations and we prove the consistency and the asymptotic normality of its QMLE.