Parameter Update Schemes for Hidden Markov Models applied to Financial Returns

Abstract: This thesis was dedicated to investigating the use of different parameter update schemes for Hidden Markov models with time-varying parameters, with an emphasis on developing alternatives to the quasi-Newton step. The focus was on applications to financial returns, using data from the S\&P-500 and the Nikkei index, and for comparison, a trial using synthetic data was also performed. Different properties of the parameter update schemes were explored, with Predictor-Corrector and Trust-Region based methods showing promise in comparison to the quasi-Newton methods previously tried. The Trust-Region method proved to be a more stable alternative, whereas the Predictor-Corrector method showed a significant smoothing of parameter adaptation which was not replicable by using the quasi-Newton method. Additionally, manipulating the norm of the Trust-Region method proved to be a versatile tool for e.g. calibrating the persistence of the hidden states without interfering with other parameter updates.