Kalman Filter and Time Series

The Kalman filter is one of the classical algorithms of the statistical estimation theory. The filter is applied in a lot of fields. One of them is econometrics, especially its sphere of econometric models in which there is at least one variable which cannot be directly observed and measured. The paper presents the basic features of the Kalman filter and its application in time series analysis. The text specifically focuses on possibilities of transformations of ARMA models into state-space form, and the following application of the Kalman filter in solving problems of prediction, filtering and smoothing. Another issue which is focused on is an application of the Kalman filter in estimating of unknown parameters of time series models. The presented procedures are demonstrated on practical problems which are implemented in the MATLAB environment; the outputs are presented in the text.