Some New Alternative Formulations of Adaptive Kalman Filter for Market Risk Beta Estimation

Kalman filter (KF) provides optimal beta estimate with linear models where the noise covariances are known a priori. Noise covariance adaptation-based adaptive KFs (AKFs) have also been used to get these beta estimates. These AKFs suffer from one typical problem, namely inadequate noise filtering. This paper explores some new formulation of such AKFs to solve this problem in addition to applying other related existing formulations. The proposed methods have been analysed through simulation study along with empirical performance verifications through VaR backtesting, expected shortfall analysis, and in-sample performance analysis. Results show that two new and one existing AKFs are successful to provide smooth beta estimates.