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### A Sequential Semiparametric Estimation for Nonlinear Function in the Functional Autoregressive Model

#### Affiliations

• Department of Statistics, Science and Research Branch, Islamic Azad University, Tehran, Iran, Islamic Republic of
• Department of Mathematics, Iran University of science and technology, Tehran - 16846, Iran, Islamic Republic of
• Department of Statistics, Chalus Branch, Islamic Azad University, Chalus, Iran, Islamic Republic of

#### Abstract

Background/Objectives: The study aimed to predict regression function using semi-recursive kernel method in the first order functional auto regressive model through semiparametric estimation. Methods/Statistical Analysis: The parametric estimation by conditional nonlinear least squares method conducted; further, regression adjustment has been estimated by recursive smooth kernel approach and then investigate weak consistencies of the estimator; In this case, simulated results are presented using recursive kernel method for the semiparametric estimation. The Average Squared Error (ASE) computed to show the efficiency of the proposed estimation method. Finding: Updating causes considerably less computations in the semiparametric estimation when a sample of size n-1 changes to one of size n, this paper for estimating the adjustment factor proposed the recursive kernel method. The accuracy of the suggested method was tested by results of simulated study. Applications: The first order functional autoregressive model is currently used in financial and econometric studies. We propose semi-recursive semi parametric method for estimating this model and the results show that the semiparametric estimator of the auto regression function performs well.

#### Keywords

Conditional Nonlinear Least Squares Method, Functional Autoregressive Model, Recursive Kernel Method, Semiparametric Estimation.

#### Full Text:

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