Estimation of an autoregressive semiparametric model with exogenous variables
type: Item
instance of: scholarly article
title: Estimation of an autoregressive semiparametric model with exogenous variables
zbMATH Open document ID: 0951.62031
DOI: 10.1016/S0378-3758(97)00137-7
author: Denis Bosq
author: Jia Shen
published in: Journal of Statistical Planning and Inference
publication date: 1999-08-23T00:00:00Z
review text: The authors deal with the estimation of an autoregressive semiparametric model \[ X_{t+1}= \varphi(X_t, \dots,X_{t-r+1})+ \psi(Y_t)+ \varepsilon_t, \] where \(\varphi\) and \(\psi\) are unknown nonlinear functions and \(\{Y_t\}\) is an exogenous variable. Two special cases are considered: (1) \(\psi\) is linear \(\psi(Y_t)= AY_t\) with an unknown parameter \(A\); (2) \(\psi\) is nonlinear corresponding to a series expansion. One first estimates parametrically the exogenous part \(\psi(\cdot)\), and then estimates nonparametrically the endogeneous part \(\varphi(\cdot)\). The a.s. and \(L_s\) convergence results are given. Numerical simulations demonstrate the method.
Mathematics Subject Classification ID: 62G08
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62M99
zbMATH DE Number: 1327281
zbMATH Keywords: exogeneous variables
zbMATH Keywords: kernel nonparametric estimation
zbMATH Keywords: semi-nonparametric
zbMATH Keywords: autoregressive semiparametric model
zbMATH Keywords: nonlinear
reviewed by: Tomáš Cipra
MaRDI profile type: Publication
cites work: Asymptotics for Semiparametric Econometric Models Via Stochastic Equicontinuity
cites work: Q3973913
cites work: Bernstein-type large deviations inequalities for partial sums of strong mixing processes
cites work: Asymptotic estimation of a non-linear infinite filter. application to the estimation of volterra series
cites work: Nonparametric statistics for stochastic processes
cites work: Tests of Noncausality under Markov Assumptions for Qualitative Panel Data
cites work: A note on the geometric ergodicity of a Markov chain
cites work: On the use of the deterministic Lyapunov function for the ergodicity of stochastic difference equations
cites work: Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations
cites work: Tail behaviour of the stationary density of general non-linear autoregressive processes of order 1
cites work: Q4856136
cites work: Estimation de la transition de probabilité d'une chaîne de Markov Doeblin-recurrente. Étude du cas du processus autoregressif général d'ordre 1
cites work: Q3999128
cites work: Exogeneity
cites work: A Note on Noncausality
cites work: Seminonparametric Estimation of Conditionally Constrained Heterogeneous Processes: Asset Pricing Applications
cites work: Q4039983
cites work: Comparing nonparametric versus parametric regression fits
cites work: Q5801713
cites work: Geometric ergodicity of Harris recurrent Markov chains with applications to renewal theory
cites work: On Transverse Vibrations of a Variable Composite Flywheel with Optimum Design
cites work: Current developments in time series modelling
cites work: Root-N-Consistent Semiparametric Regression
cites work: Q4717186
cites work: The existence of moments for stationary Markov chains
cites work: Non-linear time series and Markov chains
cites work: Q4307738
cites work: Moment bounds for stationary mixing sequences
description: scientific article; zbMATH DE number 1327281