Estimation, prediction, and interpolation for ARIMA models with missing data. (English) Zbl 0607.62106

Kohn, Robert; Ansley, Craig F.

J. Am. Stat. Assoc. 81, 751-761 (1986).

The paper investigates non-stationary Gaussian autoregressive integrated moving average (ARIMA) time series models with missing observations. The marginal likelihood is defined and computed efficiently for these models. The definition of the likelihood for a non-stationary time series model is based on the concept of a marginal likelihood. This definition of the likelihood is invariant under a large class of transformations and if there are no missing observations this definition coincides with the definition given by Box and Jenkins.
The computation of the marginal likelihood is carried out by using the univariate version of the modified Kalman filter introduced earlier by the authors [J. Stat. Comput. Simulation 21, 135-169 (1985; Zbl 0595.62092)]. The paper shows how to predict and interpolate missing observations and obtain the mean squared error of the estimate.

Reviewer: I.G.Zhurbenko

MSC:

62M10	Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20	Inference from stochastic processes and prediction

Keywords:

estimation; prediction; diffuse initial conditions; maximum likelihood; transformation invariant likelihood; non-stationary Gaussian autoregressive integrated moving average (ARIMA) time series; missing observations; marginal likelihood; modified Kalman filter; mean squared error

Software:

AS 154