Abstract: Hidden Markov model (HMM) has been widely applied to many fields. This paper tries to improve current HMMs from different aspects and then applies the improved HMM to financial forecasting. Firstly, by fixing the initial points for the K-means clustering algorithm so that its clustering results are more stable, we use the resulting K-means clustering algorithm to seek better initial values for the Baum-Welch algorithm. To improve the forecasting accuracy, we apply the following new techniques: we choose the model parameters obtained from the Baum-Welch algorithm as the inputs for the Vertibi algorithm to determine the optimal sequence of the hidden states, and we repartition the observing vector. Then we determine the sets of observing vectors corresponding to the different hidden states. Based on the outputs of the Vertibi algorithm, we recompute the means and variances of different classes of observing vectors. The resulting mean vector and variance-covariance matrix are taken as the initial values for the Baum-Welch algorithm, which finally finds the optimal model parameters for HMM. Last but not least, instead of the existing methods seeking similar movements of the practice in the historical interval, we not only obtain the fine expression step of conditional probability, and by maximizing the conditional probability values, we derive better predictive value. Numerical results based on the real trading data of Chinese stock markets indicate the superiority of the improved HMM. 

Key words: hidden Markov model, K-means clustering algorithm, hidden state, model parameters, financial forecasting