This thesis applies the time-varying signal processing models to track the multifactor systematic risk in the Fama-French model. The mean reverting, random walk and random coefficient models are used to analyze the time-varying multifactor beta based on the multivariate Kalman filter algorithm. The sudden changes in the mutifactor beta ar e captured by the piecewise constant model. Our case studies explain the impacts of economic events on the sudden changes in betas for both individual stocks and industrial portfolios.
We propose a new time-varying beta model based on a piecewise mean reverting process to express the effects of different types of events on the multifactor beta.The tracking of the piecewise mean reverting beta, using the modified multivariate Kalman filter with the maximum log likelihood estimator, outperforms the traditional piecewise constant and random walk models as demonstrated in our simulations. The empirical tests indicate that the new model effectively captures the different changes in beta depending on the type of event.
The Estimation of Parameters to minimize the Energy Function of the Piecewise Constant Model Using Three-way Analysis of Variance
