Estimating Missing Observations in Economic Time Series

Abstract

Two related problems are considered. The first concerns the maximum likelihood estimation of the parameters in an ARIMA model when some of the observations are missing or subject to temporal aggregation. The second concerns the estimation of the missing observations. Both problems can be solved by setting up the model in state space form and applying the Kalman filter.

Computing Missing Values in Time Series

“…Then, in order to estimate the missing values the fixed point smoother can be used. This approach was extended by Ansley and Kohn (1983), Harvey and Pierse (1984) and Ansley (1983, 1986), to the nonstationary case. The numerical problems involved in the maximization of the likelihood were analyzed by Wincek an4 Reinsel (1986).…”

Temporal disaggregation using multivariate structural time series models

“…Though modelling the series in logs creates no difficulties for stock variables, for flow series no simple solution exists at the moment simply because, for the aggregated variable, the logarithm of the sum is not equal to the sum of the logarithms. As suggested in Harvey and Pierce (1984), one way to proceed would be to assume that the logarithms of the variables are normally distributed, then to modify accordingly the state-space representation of the model, and finally to use the extended Kalman filter to obtain an approximation to the likelihood function computed by the prediction error decomposition.…”

Measuring Influence in Dynamic Regression Models

“…Jones (1980), Harvey and Pierce (1984), and Kohn and Ansley (1986) have shown how to solve this problem by setting up the model in state space form and applying the KaIman filter. An alternative method is the following.…”