Hidden Markov model and financial application
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A Hidden Markov model (HMM) is a statistical model in which the system being modeled is assumed to be a Markov process with numerous unobserved (hidden) states. This report applies HMM to financial time series data to explore the underlying regimes that can be predicted by the model. These underlying regimes can be used as an important signal of market environments and used as guidance by investors to adjust their portfolio to maximize the performance. This report is composed of three chapters. The 1st chapter will introduce the difficulties in predicting financial time series, the limitations with traditional time series models, justification for choosing HMM and previous studies. The 2nd chapter will go through a detailed overview of HMM model, including the basic math frame works, and fundamental questions and algorithm to be addressed by the model. In the 3rd chapter, the trend analysis of the stock market is found using Hidden Markov Model. For a given observation sequence, the hidden sequence of states and their corresponding probability values are found. This analysis builds a platform for investors to decision makers to make decisions on the basis of probability and pattern of transition of each hidden state which cannot be observed from market data.