Estimation of missing values in possibly partially nonstationary vector time series

Ljung's(1989) method for estimating missing values and evaluating the corresponding likelihood function in scalar time series is extended to the vector case. The series is assumed to be generated by a possibly partially nonstationary and noninvertible vector autoregressive-moving average process. No particular pattern of missing data is assumed. Future and past values are special cases of missing data that can be estimated in the same way. The method does not use Kalman filter iterations and hence avoids initialisation problems. It does not require the series to be differenced and thus avoids complications caused by over-differencing. The estimators of the missing data are provided by the normal equations of an appropriate regression problem. These equations are adapted to cope with temporally aggregated data; the procedure parallels a matrix treatment of contour conditions in the analysis of variance. Autoregressive processes are considered in some detail.