Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model
Open Access
- 4 August 2021
- journal article
- research article
- Published by VTeX in Modern Stochastics: Theory and Applications
- Vol. 8 (4), 435-463
- https://doi.org/10.15559/21-vmsta187
Abstract
Publisher: VTeX - Solutions for Science Publishing, Journal: Modern Stochastics - Theory and Applications, Title: Bias reduction of a conditional maximum likelihood estimator for a Gaussian second-order moving average model, Authors: Fumiaki Honda, Takeshi Kurosawa , In this study, we consider a bias reduction of the conditional maximum likelihood estimators for the unknown parameters of a Gaussian second-order moving average (MA(2)) model. In many cases, we use the maximum likelihood estimator because the estimator is consistent. However, when the sample size n is small, the error is large because it has a bias of $O({n^{-1}})$. Furthermore, the exact form of the maximum likelihood estimator for moving average models is slightly complicated even for Gaussian models. We sometimes rely on simpler maximum likelihood estimation methods. As one of the methods, we focus on the conditional maximum likelihood estimator and examine the bias of the conditional maximum likelihood estimator for a Gaussian MA(2) model. Moreover, we propose new estimators for the unknown parameters of the Gaussian MA(2) model based on the bias of the conditional maximum likelihood estimators. By performing simulations, we investigate properties of this bias, as well as the asymptotic variance of the conditional maximum likelihood estimators for the unknown parameters. Finally, we confirm the validity of the new estimators through this simulation study.
Keywords
This publication has 11 references indexed in Scilit:
- A general result on the estimation bias of ARMA modelsJournal of Statistical Planning and Inference, 2018
- Bias reduction of the maximum-likelihood estimator for a conditional Gaussian MA(1) modelCommunications in Statistics - Theory and Methods, 2017
- Finite-Sample Bias of the Conditional Gaussian Maximum Likelihood Estimator in ARMA ModelsPublished by Emerald ,2016
- Improved prediction limits for a general class of Gaussian modelsJournal of Time Series Analysis, 2010
- Expectation of quadratic forms in normal and nonnormal variables with applicationsJournal of Statistical Planning and Inference, 2010
- The second-order bias and mean squared error of estimators in time-series modelsJournal of Econometrics, 2007
- Bias Reduction of Autoregressive Estimates in Time Series Regression Model through Restricted Maximum LikelihoodJournal of the American Statistical Association, 2000
- Bias correction in ARMA modelsStatistics & Probability Letters, 1994
- Asymptotic Expansions Associated with the AR(1) Model with Unknown MeanEconometrica, 1983
- Likelihood Function of Stationary Multiple Autoregressive Moving Average ModelsJournal of the American Statistical Association, 1979