Replacement of missing values in time series data by Kalman smoothed estimators using state-space modeling.

Procedures for estimation of the parameters in linear models allow for missing observations in the dependent and independent variables. In serially correlated data, an alternative approach to model the data is to use time series analysis techniques. However, generally available programs for Autoregressive Integrated Moving Average (ARIMA) time series analysis assume measurements at fixed intervals. Therefore, they do not allow for randomly missing observations. Ad-hoc techniques such as exponential smoothing, polynomials, and symmetric moving averages have also been applied to time series data (Gardner, 1985). The general state-space model (Ljung, 1987) is a time series technique which can be used to estimate missing values (Shumway and Stoffer, 1982). This paper reviews the statespace model, introduces a computer program to estimate missing values, and illustrates its use with a specific example.