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In the present article, we propose and study a new class of nonlinear autoregressive moving-average (ARMA) models, in which each moving-average (MA) coefficient is enlarged to an arbitrary univariate function. We first provide a sufficient condition for the existence of the stationary solution and further discuss the moment structure. We investigate the estimation method to the proposed models. The global estimates of parameters and local linear estimates of functional coefficients are obtained by using a back-fitting algorithm. For testing whether the functional coefficients are some specified parametric forms, a bootstrap test approach is provided. The proposed models are illustrated by both simulated and real data examples.

Parameter estimation and subset selection for separable lower triangular bilinear (SLTBL) models are considered. Under a flat prior, we present an expectation–maximization (EM) algorithm to obtain the maximum likelihood estimation. Furthermore, two sub-procedures are designed to select the best subset model after an initial fitting. Example with two simulated and one real data set illustrate the feasibility and validity of the proposed methods.