Inference for some time series models with random coefficients and infinite variance innovations

Infinite variance processes have attracted growing interest in recent years due to their applications in many areas of statistics. For example, ARIMA time series models with infinite variance innovations are widely used in financial modelling. However, little attention has been paid to incorporate infinite variance innovations for time series models with random coefficients introduced by Nicholls and Quinn. Estimation of model parameters for some special cases is discussed using the least absolute deviation (LAD) estimating function approach when the closed form density is available. It is also shown that these new LAD estimates are superior to some of the existing ones.