Adaptive Estimation and Filtering in Finance

Some salient contributions of this work are modification and characterization of Adaptive Kalman Filter (AKF) and application thereof in modelling and estimation of financial time series. The failure cases of AKF's have been identified and characterized. Modifications are then made to avoid the singularity, without affecting the essential performance of AKFs. These modified varieties of AKF techniques were characterized using both synthetic data and empirical data from Indian financial market. Performances of the existing and modified AKF methods are compared with the benchmark approaches and conventional adaptive methods (like Recursive Least Square and Least Mean Square) for beta and volatility (and hence VaR) estimation. Performances of the conventional and evolved adaptive methods have been compared with the performances of benchmark methods and advantages of the adaptive methods have been pointed out. The analysis would hopefully provide better understanding of Indian financial markets and permit better financial decisions.