Estimation for some bilinear time series

The first part of this paper is concerned with bilinear time series with innovations having infinite variance. A Least Gamma Deviation (LGD) estimation procedure is proposed for the inference of the parameters of some bilinear time series with infinite variance innovations and shown to be strongly consistent. Numerical simulations demonstrate the superiority of this new procedure to the conventional Least Squares (LS) procedure. The concepts of causality and invertibility are also briefly discussed. In the remainder of this paper, attention is focused on the derivation of the asymptotic distributions of the least squares estimates under finite variance assumptions.