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Missing Values

The TIMSAC subroutines skip any missing values at the beginning of the data set. When the univariate and multivariate AR models are estimated via least squares (TSMLOCAR, TSMLOMAR, TSUNIMAR, TSMULMAR, and TSPEARS), there are three options available; that is, MISSING=0, MISSING=1, or MISSING=2. When the MISSING=0 (default) option is specified, the first contiguous observations with no missing values are used. The MISSING=1 option specifies that only nonmissing observations should be used by ignoring the observations with missing values. If the MISSING=2 option is specified, the missing values are filled with the sample mean. The least squares estimator with the MISSING=2 option is biased in general.

The BAYSEA subroutine assumes the same prior distribution of the trend and seasonal components that correspond to the missing observations. A modification is made to skip the components of the vector that correspond to the missing observations. The vector is defined in the section "Bayesian Constrained Least Squares". In addition, the TSBAYSEA subroutine considers outliers as missing values. The TSDECOMP and TSTVCAR subroutines skip the Kalman filter updating equation when the current observation is missing.