A semiparametric first-order nonlinear autoregressive model with dependent and skew normal errors

The common ways for analyzing the nonlinear autoregressive models are based on normality assumption of errors, whereas in many practical situations, the residuals show a nonnormal structure. The use of these methods leads to misleading and unreliable forecasts. Also, in these conditions, parametric and nonparametric methods do not have the necessary efficiency in estimating the nonlinear regression function. In this paper, a first-order nonlinear autoregressive model with dependent skew normal errors is introduced and a semiparametric method is proposed to estimate the nonlinear part of model. The parameters are estimated by the maximum likelihood (ML) method using Expectation-Maximization (EM) algorithm. The performance of the proposed model is investigated by a simulation study and analysis of a real data set of daily data on the exchange rate of the euro to the dollar.