Miscellanea. Estimation of missing values in possible partially nonstationary vector time series
将Ljung(1989)的标量时间序列缺失值估计方法推广到向量情形,适用于可能部分非平稳和非可逆的VARMA过程,无需卡尔曼滤波迭代或差分处理,通过回归问题的正规方程提供估计量。
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.