Testing the functions defining a nonlinear autoregressive time series
type: Item
instance of: scholarly article
title: Testing the functions defining a nonlinear autoregressive time series
zbMATH Open document ID: 0704.62083
DOI: 10.1016/0304-4149(90)90044-S
author: J. Diebolt
published in: Stochastic Processes and their Applications
publication date: 1990-01-01T00:00:00Z
review text: The author considers a stationary random sequence \((X_ n\); \(n\geq 1)\), given by \[ X_{n+1}=T(X_ n)+U(X_ n)\epsilon_{n+1}, \] where T and U are real functions, \(U>0\), and \((\epsilon_ n\); \(n\geq 1)\) is a stationary \(\phi\)-mixing sequence with zero expectation and unit variance. Estimators of T and U of the regressogram type are defined and their consistency is proved. A functional limit theorem related to the estimators is derived. Nonparametric goodness-of-fit tests for T and U are presented. The results are illustrated by numerical simulation.
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G10
Mathematics Subject Classification ID: 60F17
zbMATH DE Number: 4155717
zbMATH Keywords: nonlinear autoregressive time series
zbMATH Keywords: regressogram type estimators
zbMATH Keywords: convergence in distribution
zbMATH Keywords: Wiener process
zbMATH Keywords: phi-mixing
zbMATH Keywords: stationary random sequence
zbMATH Keywords: consistency
zbMATH Keywords: functional limit theorem
zbMATH Keywords: goodness-of-fit tests
zbMATH Keywords: numerical simulation
reviewed by: Jiří Anděl
MaRDI profile type: Publication
cites work: Q3036531
cites work: Prediction using non-parametric techniques: some comparisons
cites work: Q5560061
cites work: Q4084479
cites work: Q3658976
cites work: Q3777169
cites work: Propri�t�s de convergence presque compl�te du pr�dicteur � noyau
cites work: Jfon parametric time series analysis and prediction: uniform almost sure convergence of the window and jt-nn autoregression estimates
cites work: Strong uniform convergence rates in robust nonparametric time series analysis and prediction: Kernel regression estimation from dependent observations
cites work: Q5822308
cites work: Q3969746
cites work: Q3871680
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: Une mesure de la déviation quadratique d'estimateurs non paramétriques. (A measure of quadratic deviation of nonparametric estimators)
cites work: Q4158357
cites work: Nonlinear autoregressive processes
cites work: Q3948500
cites work: Q3851319
cites work: On the Speed of Convergence in a Boundary Problem. I
cites work: STATE-DEPENDENT MODELS: A GENERAL APPROACH TO NON-LINEAR TIME SERIES ANALYSIS
cites work: NONPARAMETRIC ESTIMATORS FOR TIME SERIES
cites work: Q3928089
cites work: Q3928091
cites work: Q3290184
cites work: Nonparametric Density Estimation, Prediction, and Regression for Markov Sequences
cites work: A comparison of Kriging with nonparametric regression methods
description: scientific article; zbMATH DE number 4155717