Widely linear prediction for transfer function models based on the infinite past

The problem of widely linear (WL) prediction for both WL ARMA models and WL transfer function models on the basis of infinite past information is studied. A recursive algorithm to obtain a suboptimum predictor for WL ARMA systems is first given. Then this algorithm is used to develop another recursive algorithm which performs WL prediction for transfer function models. The suggested solutions become an alternative to the WL prediction based on a finite number of observations provided the size of the time series is sufficiently large.