Nonlinear semiparametric autoregressive models based on a class of two-piece distributions

In this study, we examined the well-known nonlinear autoregressive time series model in which innovations follow the flexible class of two-piece distributions based on the scale mixtures of normal (TP-SMN) family. The mentioned class of distributions is a rich class of distributions family that covers the robust symmetric/asymmetric light/heavy-tailed distributions. The nonlinear part of the autoregressive time series model is estimated via the semiparametric and nonparametric curve estimation based on the conditional least square method and nonparametric kernel approach. The maximum likelihood (ML) estimates of the model parameters, using a suitable hierarchical representation of the TP-SMN family on the model are obtained via an expectation-maximization type algorithm. Performances and usability of the proposed model and estimates are shown through simulation studies and a real dataset.