Parameter estimation of an asset price model driven by a weak hidden Markov chain

We introduce a weak hidden Markov model (WHMM) in an attempt to capture more accurately the evolution of a risky asset. The log returns of assets are modulated by a weak or higher-order Markov chain with finite-state space. In particular, the optimal estimates of the second-order Markov chain and parameters of the model are given in terms of the discrete-time filters for the state of the Markov chain, the number of jumps, occupation time and auxiliary processes. We provide a detailed implementation of the model to a dataset of financial time series along with the analysis of the h-day ahead forecasts. The results of our error analysis suggest that within the dataset studied and considering longer predictive horizons, WHMM gives a better forecasting performance than the traditional HMM.