A Semiparametric Estimation for Regression Functions in the Partially Linear Autoregressive Time Series Model

Authors

R. Farnoosh, Iran University of Science and Technology
M. Hajebi, Iran University of Science and Technology
S. J. Mortazavi, Islamic Azad University of Science and Research

Abstract

In this paper, a semiparametric method is proposed for estimating regression function in the partially linear autoregressive time series model . Here, we consider a combination of parametric forms and nonlinear functions, in which the errors are independent. Semiparametric and nonparametric curve estimation provides a useful tool for exploring and understanding the structure of a nonlinear time series data set to make for a more efficient study in the partially linear autoregressive model. The unknown parameters are estimated using the conditional nonlinear least squares method, and the nonparametric adjustment is also estimated by defining and minimizing the local L2 -fitting criterion with respect to the nonparametric adjustment and, with smooth-kernel method , these estimates are corrected. Then, the autoregression function estimators, which can be calculated with the sample and simulation data , are obtained. In this case , some strong and weak consistency and simulated results for the semiparametric estimation in this model are presented . The root mean square error and the average square error criterions are also applied to verify the efficiency of the suggested model .

Recommended Citation

Farnoosh, R.; Hajebi, M.; and Mortazavi, S. J. (2014). A Semiparametric Estimation for Regression Functions in the Partially Linear Autoregressive Time Series Model, Applications and Applied Mathematics: An International Journal (AAM), Vol. 9, Iss. 2, Article 9.
Available at: https://digitalcommons.pvamu.edu/aam/vol9/iss2/9