A semiparametric method for estimating nonlinear autoregressive model with dependent errors (original) (raw)
Related papers
A Semiparametric Estimation for the Nonlinear Vector Autoregressive Time Series Model
2017
In this paper, the nonlinear vector autoregressive model is considered and a semiparametric method is proposed to estimate the nonlinear vector regression function. We use Taylor series expansion up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the parameters are estimated through the least squares method, the obtained nonlinear vector regression function is adjusted by a nonparametric diagonal matrix, and the proposed diagonal matrix is also estimated through the nonparametric smooth-kernel approach. Estimating the parameters can yield the desired estimate of the vector regression function based on the data. Under some conditions, the asymptotic consistency properties of the proposed semiparametric method are established. In this case, some simulated results for the semiparametric estimators in a nonlinear vector autoregressive function are presented. Mean Squares Error (MSE) criterion is also applied to ...
A semiparametric approach for modelling multivariate nonlinear time series
Canadian Journal of Statistics, 2019
In this article, a semiparametric time-varying nonlinear vector autoregressive (NVAR) model is proposed to model nonlinear vector time series data. We consider a combination of parametric and nonparametric estimation approaches to estimate the NVAR function for both independent and dependent errors. We use the multivariate Taylor series expansion of the link function up to the second order which has a parametric framework as a representation of the nonlinear vector regression function. After the unknown parameters are estimated by the maximum likelihood estimation procedure, the obtained NVAR function is adjusted by a nonparametric diagonal matrix, where the proposed adjusted matrix is estimated by the nonparametric kernel estimator. The asymptotic consistency properties of the proposed estimators are established. Simulation studies are conducted to evaluate the performance of the proposed semiparametric method. A real data example on short-run interest rates and long-run interest rates of United States Treasury securities is analyzed to demonstrate the application of the proposed approach.
A comparative study of parametric and semiparametric autoregressive models
International Journal of Accounting and Economics Studies
Dynamic linear regression models are used widely in applied econometric research. Most applications employ linear autoregressive (AR) models, distributed lag (DL) models or autoregressive distributed lag (ARDL) models. These models, however, perform poorly for data sets with unknown, complex nonlinear patterns. This paper studies nonlinear and semiparametric extensions of the dynamic linear regression model and explores the autoregressive (AR) extensions of two semiparametric techniques to allow unknown forms of nonlinearities in the regression function. The autoregressive GAM (GAM-AR) and autoregressive multivariate adaptive regression splines (MARS-AR) studied in the paper automatically discover and incorporate nonlinearities in autoregressive (AR) models. Performance comparisons among these semiparametric AR models and the linear AR model are carried out via their application to Australian data on growth in GDP and unemployment using RMSE and GCV measures. Â
Advances in Mathematical Physics, 2022
The nonlinear autoregressive models under normal innovations are commonly used for nonlinear time series analysis in various fields. However, using this class of models for modeling skewed data leads to unreliable results due to the disability of these models for modeling skewness. In this setting, replacing the normality assumption with a more flexible distribution that can accommodate skewness will provide effective results. In this article, we propose a partially linear autoregressive model by considering the skew normal distribution for independent and dependent innovations. A semiparametric approach for estimating the nonlinear part of the regression function is proposed based on the conditional least squares approach and the nonparametric kernel method. Then, the conditional maximum-likelihood approach is used to estimate the unknown parameters through the expectation-maximization (EM) algorithm. Some asymptotic properties for the semiparametric method are established. Finally...
Estimation in Semiparametric Time Series Models
SSRN Electronic Journal, 2000
In this paper, we consider a semiparametric time series regression model and establish a set of identification conditions such that the model under discussion is both identifiable and estimable. We estimate the parameter in the model by using the method of moment and the nonlinear function by using the local linear method, and establish the asymptotic distributions for the proposed estimators. We then discuss how to estimate a sequence of local departure functions nonparametrically when the null hypothesis is rejected and establish some related asymptotic theory. The simulation study and empirical application are also provided to illustrate the finite sample behavior of the proposed methods.
Nonparametric estimation for an autoregressive model
The paper deals with the nonparametric estimation problem at a given fixed point for an autoregressive model with unknown distributed noise. Kernel estimate modifications are proposed. Asymptotic minimax and efficiency properties for proposed estimators are shown.
Adaptive estimators in nonparametric autoregressive models
2009
This paper deals with the estimation of a autoregression function at a given point in nonparametric autoregression models with Gaussian noise. An adaptive kernel estimator which attains the minimax rate is constructed for the minimax risk.
2011
The goal of this work is to develop a nonparametric conditional heteroscedastic autoregressive nonlinear (NCHARN) model by using maximum likelihood method that not only account for possibly non-linear trend but also account for possibly non-linear conditional variance of response as a function of predictor variables in the presence of auto-correlated errors. The trend and the heteroscedasticity are modeled using a class of penalized spline and the residuals are modeled as a autoregressive process (AR) by selecting an appropriate number of lag residuals. Both classical penalized spline and AR process of penalized spline under NCHARN model are developed to obtain the smooth estimates of the conditional mean and variance functions. The resulting estimated values are then used the maximum likelihood method to fi t a trend, volatility, and a coeffi cient of AR process by suitably choosing the order of AR using the Akaike Information Criteria (AIC). The forecasting performance of the prop...