Abstract
This paper is divided into two parts: (i) to give a mathematical description for a class of nonlinear MA models, which is expected to be a good basic model in case of fitting the data whose outstanding feature lies in sporadically large values such as observed in geo-physical, turbulence data, etc.; and (ii) to propose a method for identification of unknown parameters in the proposed nonlinear MA model.
First, a class of nonlinear MA models is proposed whose nonlinear terms are described by a set of Hermite orthogonal functions. Secondly, a method is presented for estimating unknown parameters by using the moment method, and asymptotic properties of the proposed estimators are mathematically investigated. Finally, salient features of the proposed nonlinear MA model and the estimators of unknown parameters are discussed from both qualitative and quantitative points of view.
