The first order nonlinear autoregressive model ‎ ‎with Ornstein Uhlenbeck processes driven by white ‎noise

Publish Year: 1400
نوع سند: مقاله ژورنالی
زبان: English
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JR_JMMF-1-1_001

تاریخ نمایه سازی: 17 فروردین 1400

Abstract:

This paper presents a nonlinear autoregressive model with ‎Ornstein ‎Uhlenbeck processes innovation driven with white noise. ‎‎‎‎Notations ‎and ‎preliminaries ‎are ‎presented ‎about ‎the ‎Ornstein ‎Uhlenbeck ‎processes ‎that ‎have ‎important ‎applications ‎in ‎finance. ‎The ‎parameter ‎estimation ‎for ‎these ‎processes ‎is ‎constructed ‎from ‎the ‎time ‎continuous ‎likelihood ‎function ‎that ‎leads ‎to ‎an ‎explicit ‎maximum ‎likelihood ‎estimator.‎ A semiparametric method is proposed to estimate the nonlinear autoregressive function using the conditional least square method for parametric estimation and the nonparametric kernel approach by using the nonparametric factor that is derived by a local L2-fitting criterion for the regression adjustment ‎estimation‎‎‎. Then the ‎Monte ‎Carlo‎‎ numerical simulation studies are carried out to show the efficiency and accuracy of the present ‎work.‎ The ‎mean square error (‎MSE) is a measure of the average squared deviation of the ‎estimated ‎function‎ values from the actual ones. The values of MSE indicate ‎that ‎the ‎innovation ‎in ‎noise ‎structure ‎is ‎performed ‎well ‎in ‎comparison ‎with ‎the ‎existing ‎noise ‎in ‎the ‎nonlinear ‎autoregressive ‎models.‎ ‎‎‎

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Authors

Parisa Nabati

Faculty of science, Urmia university of technology, Urmia,Iran