Noninvertibility and Pseudo-Maximum Likelihood Estimation of Misspecified ARMA Models
- 1 September 1991
- journal article
- research article
- Published by Cambridge University Press (CUP) in Econometric Theory
- Vol. 7 (4), 435-449
- https://doi.org/10.1017/s0266466600004692
Abstract
Recently Tanaka and Satchell [11] investigated the limiting properties of local maximizers of the Gaussian pseudo-likelihood function of a misspecified moving average model of order one in case the spectral density of the data process has a zero at frequency zero. We show that pseudo-maximum likelihood estimators in the narrower sense, that is, global maximizers of the Gaussian pseudo-likelihood function, may exhibit behavior drastically different from that of the local maximizers. Some general results on the limiting behavior of pseudo-maximum likelihood estimators in potentially misspecified ARMA models are also presented.Keywords
This publication has 10 references indexed in Scilit:
- ESTIMATION OF AUTOREGRESSIVE MOVING‐AVERAGE ORDER GIVEN AN INFINITE NUMBER OF MODELS AND APPROXIMATION OF SPECTRAL DENSITIESJournal of Time Series Analysis, 1990
- Asymptotic Properties of the Maximum-Likelihood and Nonlinear Least-Squares Estimators for Noninvertible Moving Average ModelsEconometric Theory, 1989
- Convergence results for maximum likelihood type estimators in multivariable ARMA models IIJournal of Multivariate Analysis, 1989
- Convergence results for maximum likelihood type estimators in multivariable ARMA modelsJournal of Multivariate Analysis, 1987
- The behaviour of the likelihood function for ARMA modelsAdvances in Applied Probability, 1984
- The Properties of the Parameterization of Armax Systems and Their Relevance for Structural Estimation and Dynamic SpecificationEconometrica, 1983
- Parameter values of ARMA models minimising the one-step-ahead prediction error when the true system is not in the model setJournal of Applied Probability, 1983
- Vector linear time series models: corrections and extensionsAdvances in Applied Probability, 1978
- Vector linear time series modelsAdvances in Applied Probability, 1976
- The asymptotic theory of linear time-series modelsJournal of Applied Probability, 1973