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

Subject Areas : Statistics

Leila  Sakhabakhsh ¹ (Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Science and Research Unit, Tehran, Iran)
rahman  Farnoosh ² (Department of Mathematics, Faculty of Mathematics, Iran University of Science and Technology, Tehran, Iran)
Afshin  Fallah ³ (Department of Statistics, Faculty of Basic Sciences, Imam Khomeini International University, Qazvin, Iran)
Mohammad Hassan  Behzadi ⁴ (Department of Mathematics, Faculty of Basic Sciences, Islamic Azad University, Science and Research Unit, Tehran, Iran)

Received: 2021-03-03 Accepted : 2022-09-07 Published : 2022-12-22

Keywords: الگوریتم EM, مدل اتورگرسیو غیرخطی, خطاهای چوله نرمال, برآورد نیمه پارامتری,

Abstract :

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.

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