A robust class of nonlinear autoregressive models with regression function and dependent innovations using semiparametric kernel estimation

In this study, researchers examine a nonlinear autoregressive (NLAR) time-series model with regression function and dependent innovations in which the errors of the model follow the two-piece scale mixtures of normal (TP-SMN) distributions. Robustness and atypical forms of the proposed class of two-piece distributions along with the flexibility of the nonlinear autoregressive model develop desirable properties which can be applied to several types of datasets. The nonlinear regression function 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 (EM)-type algorithm. Performances and usefulness of the proposed model and estimates are shown via simulation studies and a real dataset.