A Semiparametric Estimation for the Nonlinear Vector Autoregressive Time Series Model (original) (raw)

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 semiparametric method for estimating nonlinear autoregressive model with dependent errors

Nonlinear Analysis: Theory, Methods & Applications, 2011

The first-order nonlinear autoregressive model is considered and a semiparametric method is proposed to estimate regression function. In the presented model, dependent errors are defined as first-order autoregressive AR(1). The conditional least squares method is used for parametric estimation and the nonparametric kernel approach is applied to estimate regression adjustment. In this case, some asymptotic behaviors and simulated results for the semiparametric method are presented. Furthermore, the method is applied for the financial data in Iran's Tejarat-Bank.

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.

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

A Semiparametric Approach for Modeling Partially Linear Autoregressive Model with Skew Normal Innovations

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 Regression

2010

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 then discuss how to estimate a sequence of local alternative functions nonparametrically when the null hypothesis does not hold. An asymptotic theory is established in each case. An empirical application is also included.

Semiparametric methods in nonlinear time series analysis: a selective review

Journal of Nonparametric Statistics, 2014

Time series analysis is a tremendous research area in statistics and econometrics. In a previous review, the author was able to break down up 15 key areas of research interest in time series analysis. Nonetheless, the aim of the review in this current paper is not to cover a wide range of somewhat unrelated topics on the subject, but the key strategy of the review in this paper is to begin with a core the 'curse of dimensionality' in nonparametric time series analysis, and explore further in a metaphorical domino-effect fashion into other closely related areas in semiparametric methods in nonlinear time series analysis.

A flexible semiparametric forecasting model for time series

Journal of Econometrics, 2015

In this paper, we propose a semiparametric procedure called the "Model Averaging MArginal Regression" (MAMAR) that is flexible for forecasting of time series. This procedure considers approximating a multivariate regression function by an affine combination of one-dimensional marginal regression functions. The weight parameters involved in the approximation are estimated by least squares on the basis of the first-stage nonparametric kernel estimates of the marginal regressions. Under some mild conditions, we have established asymptotic normality for the estimated weights and the regression function in two cases: Case I considers the number of the covariates is fixed while Case II allows the number of the covariates depending on the sample size and diverging. As the observations are assumed to be stationary and near epoch dependent, the approach developed is applicable to both the estimation and forecasting issues in time series analysis. Furthermore, the method and result are augmented by a simulation study and illustrated by an application in forecasting the high frequency volatility of the FTSE100 index.