ARMAX model specification testing, with an application to unemployment in the Netherlands
type: Item
instance of: scholarly article
title: ARMAX model specification testing, with an application to unemployment in the Netherlands
zbMATH Open document ID: 0621.62106
DOI: 10.1016/0304-4076(87)90086-8
author: Herman J. Bierens
published in: Journal of Econometrics
publication date: 1987-01-01T00:00:00Z
full work available at URL: http://hdl.handle.net/1871/11860
review text: The author presents a new model specification test for testing an ARMAX model specification against the alternative hypothesis that the involved ARMAX specification is false. The \((k+1)\)-variate time series process \(\{(y_ t,x_ t)\}\) with \(x_ t\) as a k-component vector is assumed to be real-valued and the error-process is denoted by \(e_ t\). Under the null it is assumed that for each t the conditional expectation of the error relative to the entire past of the process involved equals zero with probability one. Under the null the test statistic of the test is N(0,1). Given the assumption that the time series are strictly stationary, this test is consistent in the sense that the absolute value of the test statistic converges in probability to infinity if the null is false. This property ensures that asymptotically any sort of misspecification will be detected. To perform the test it is neither required that the errors are Gaussian white noise nor that they are homoscedastic. The weaker requirements imply that standard specification tests such as LR and LM and the Box- Pierce test are not applicable in a straight forward manner. Furthermore, estimation of the parameters of the vector ARMAX model with x as a vector of exogenous variables as given by \textit{E. J. Hannan}, \textit{W. T. M. Dunsmuir} and \textit{M. Deistler}, J. Multivariate Anal. 10, 275- 295 (1980; Zbl 0445.62098), cannot be applied directly here for three reasons: first, x being exogenous implies that the error process is independent of the \((x_ t)\) process so that feedback from \(y_ t\) to \(x_ t\) is excluded. Secondly, incorporating this condition in the test procedure would affect the type-I-error of the test (the true null may be rejected), and thirdly, the ARMAX structure need not hold under the alternative that the null is false. In part two of the paper the author applies this ARMAX specification test to test the rational expectations - natural rate hypothesis for the Netherlands unempl…
Mathematics Subject Classification ID: 62P20
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 4007538
zbMATH Keywords: Granger causality
zbMATH Keywords: new model specification test
zbMATH Keywords: ARMAX model specification
zbMATH Keywords: time series
zbMATH Keywords: conditional expectation
zbMATH Keywords: strictly stationary
zbMATH Keywords: misspecification
zbMATH Keywords: vector ARMAX model
zbMATH Keywords: rational expectations - natural rate hypothesis
zbMATH Keywords: Netherlands unemployment rate
MaRDI profile type: Publication
OpenAlex ID: W2791675963
cites work: A uniform weak law of large numbers under π‐mixing with application to nonlinear least squares estimation
cites work: Consistent model specification tests
cites work: Uniform Consistency of Kernel Estimators of a Regression Function Under Generalized Conditions
cites work: Model specification testing of time series regressions
cites work: Non-linear regression with discrete explanatory variables, with an application to the earnings function
cites work: Distribution of Residual Autocorrelations in Autoregressive-Integrated Moving Average Time Series Models
cites work: Martingale Central Limit Theorems
cites work: Q5545069
cites work: Forecasting and conditional projection using realistic prior distributions
cites work: Testing Against General Autoregressive and Moving Average Error Models when the Regressors Include Lagged Dependent Variables
cites work: Testing for Higher Order Serial Correlation in Regression Equations when the Regressors Include Lagged Dependent Variables
cites work: Investigating Causal Relations by Econometric Models and Cross-spectral Methods
cites work: Estimation of vector Armax models
cites work: A maximal inequality and dependent strong laws
cites work: Testing Non-Nested Nonlinear Regression Models
cites work: Q5593890
cites work: Nonlinear Regression with Dependent Observations
Recommended article: Specification testing and nonparametric estimation of the human capital model
Recommended article: Specification testing in nonparametric AR‐ARCH models
Recommended article: Q3761532
Recommended article: BOOTSTRAP ASSISTED SPECIFICATION TESTS FOR THE ARFIMA MODEL
Recommended article: Econometric Model Specification
Recommended article: Semiparametric Specification Testing of Non-nested Econometric Models
Recommended article: EXACT MAXIMUM LIKELIHOOD ESTIMATE AND LAGRANGE MULTIPLIER TEST STATISTIC FOR ARMA MODELS
Recommended article: On the Rigour of Some Misspecification Tests for Modelling Dynamic Relationships
Recommended article: Q3565329
Recommended article: Q5410403
description: scientific article; zbMATH DE number 4007538