A Bayesian Approach to Kalman Filter for Elliptically Contoured Distribution and its Application in Time Series Models

Abstract

This paper develops a Bayesian formulation of Kalman filter under the errors having elliptically contoured distributions in both observation equation and system (or state) equation, using some recent results in multivariate analysis. Estimation of parameters in case of missing observations and prediction of missing observations as well are dealt with under the above set up of autoregressive-moving average process in time series. Two illustrative examples are presented with the help of AR(1) model and ARMA (1, 1) model.