Analytical uses of Kalman filtering in econometrics — A survey

This paper surveys the different uses of Kalman filtering in the estimation of statistical (econometric) models. The Kalman filter will be portrayed as (i) a natural generalization of exponential smoothing with a time-dependent smoothing factor, (ii) a recursive estimation technique for a variety of econometric models amenable to a state space formulation in particular for econometric models with time varying coefficients (iii) an instrument for the recursive calculation of the likelihood of the (constant) state space coefficients (iv) a means of helping to implement the scoring⁻ and EM-method for iteratively maximizing this likelihood (v) an analytical tool in asymptotic estimation theory. The concluding section points to the importance of Kalman filtering for alternatives to maximum⁻ likelihood estimation of state space parameters.