چكيده به لاتين
Time series is one of the statistics and probability branches which deals with different fields of studies such as geophysics, communication engineering, financial engineering, meteorology, economics, medicine, biology, psychology, astronomy science, social science and the like.
Introduction of time series in statistics began from its univariate case and then developed to multivariate time series. In the vector time series model definition, it is tried to investigate the properties of vector time series model (for example, $m$-dimensional vector) which its steps are sequentially complicated and leads to the new statistical problems in both theoretical and applied cases. In this study, a time series model which we call vector autoregressive model, estimated by a semiparametric method. In the beginning, nonlinear vector autoregressive model is estimated and then partially linear vector autoregressive model would be estimated. Multivariate Taylor series expansion of the link function up to second order is applied to estimate the vector autoregressive function. Also, semiparametric method is suggested in these models for both independent and dependent errors. Parameters of the model can be estimated by least squares and maximum likelihood methods and then the estimated vector autoregressive function can be adjusted by the nonparametric diagonal matrix. Finally, the adjusted matrix would be estimated by using nonparametric kernel estimator. In this approach, Mean Square Errors as an efficiency criterion is applied. As it follows, consistency theorems of the semiparametric estimators in the vector autoregressive models with independent and dependent errors, will be dealt with. The goal of this research, is using of semiparametric method to estimate the unknown functions in the nonlinear and partially linear autoregressive models with independent and dependent errors which will result in high accuracy for the prediction of nonlinear time data. Also, the suggested semiparametric method which is a combination of parameters estimations and nonparametric adjusted matrix, proves the consistency of the estimator, eventually. Simulation studies and empirical applications show that the obtained estimator is efficient.
