Abstract:

Based on the EM algorithm for model parameter estimation, this paper examines the $q$-order moving average model with missing data, aiming at figuring out the estimation of missing data and its covariance matrix. The effectiveness of the proposed algorithm is verified by numerical simulation which shows the following results: the mean square error of the model parameter estimation grows with the increase of the model order, the length of model characteristic roots and the proportion of missing data respectively. In addition, the value decreases when the length of sequence increases. The mean square error of missing data grows with the increase of the model order and the length of model characteristic roots. However, it is not sensitive to the length of the sequence and the proportion of missing data. An instance illustrates that the method estimates the model well in the case of missing data.

Key words: moving average (MA) model, EM algorithm, missing data, numerical simulation