scholarly journals Yule-Walker Estimation for the Moving-Average Model

2011 ◽  
Vol 2011 ◽  
pp. 1-20 ◽  
Author(s):  
Chrysoula Dimitriou-Fakalou
Keyword(s):  
Moving Average ◽  
Likelihood Estimation ◽  
Average Process ◽  
Moving Average Process ◽  
Average Model ◽  
Standard Result ◽  
Variance Matrix ◽  
Asymptotically Normal ◽  
Moving Average Model ◽  
Moments Estimators

The standard Yule-Walker equations, as they are known for an autoregression, are generalized to involve the moments of a moving-average process indexed on any number of dimensions. Once observations become available, new moments estimators are set to imitate the theoretical equations. These estimators are not only consistent but also asymptotically normal for any number of indexes. Their variance matrix resembles a standard result from maximum Gaussian likelihood estimation. A simulation study is added to conclude on their efficiency.

Moving Average Model with an Alternative GARCH-Type Error

2018 ◽  
Vol 6 (2) ◽  
pp. 165-177
Author(s):  
Huafeng Zhu ◽  
Xingfa Zhang ◽  
Xin Liang ◽  
Yuan Li
Keyword(s):  
Moving Average ◽  
Real Data ◽  
Likelihood Estimator ◽  
Average Model ◽  
Data Set ◽  
Moment Conditions ◽  
Asymptotically Normal ◽  
Moving Average Model ◽  
Simulation Results ◽  
Quasi Maximum Likelihood

Abstract Motivated by the double autoregressive model with order p (DAR(p) model), in this paper, we study the moving average model with an alternative GARCH error. The model is an extension from DAR(p) model by letting the order p goes to infinity. The quasi maximum likelihood estimator of the parameters in the model is shown to be asymptotically normal, without any strong moment conditions. Simulation results confirm that our estimators perform well. We also apply our model to study a real data set and it has better fitting performance compared to DAR model for the considered data.

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