Abstract:
The problem of estimating the parameters of an autoregressive moving average (ARMA) process based on a time series with missing observations, is considered. This paper describes a solution of the problem by using the state space approach. The method of calculating the exact likelihood function of a ARMA time series based on the state space representation and using Kalman recursive estimation, is modified to accommodate the missing values. This is accomplished via the prediction error decomposition of the likelihood function. Other possible methods for handling time series with missing data are discussed. Of these, four are chosen for numerical comparison of the results obtained by the state space approach. The main conclusion that is drawn is that several techniques, including the state space approach, appear to perform equally well for shorter stretches of missing data, and equally poor for longer stretches.
