Smoothed estimates for models with random coefficients and infinite variance innovations

Abstract

Infinite variance processes have attracted growing interest in recent years due to its applications in many areas of statistics (see [1] and references therein). For example, ARIMA time-series models with infinite variance innovations are widely used in financial modelling. However, a little attention has been paid to incorporate infinite variance innovations for time-series models with random coefficients introduced by [2]. This paper considers the problem of nonparametric estimation for some time-series models using the smoothed least absolute deviation (SLAD) estimating function approach. We introduce a class of kernels in order to smooth the LAD estimators. It is also shown that this new SLAD estimators are superior than some existing ones.