Comparative Analysis of the Hidden Markov Model and LSTM: A Simulative Approach

Time series and sequential data have gained significant attention recently since many real-world processes in various domains such as finance, education, biology, and engineering can be modeled as time series. Although many algorithms and methods such as the Kalman filter, hidden Markov model, and long short term memory (LSTM) are proposed to make inferences and predictions for the data, their usage significantly depends on the application, type of the problem, available data, and sufficient accuracy or loss. In this paper, we compare the supervised and unsupervised hidden Markov model to LSTM in terms of the amount of data needed for training, complexity, and forecasting accuracy. Moreover, we propose various techniques to discretize the observations and convert the problem to a discrete hidden Markov model under stationary and non-stationary situations. Our results indicate that even an unsupervised hidden Markov model can outperform LSTM when a massive amount of labeled data is not available. Furthermore, we show that the hidden Markov model can still be an effective method to process the sequence data even when the first-order Markov assumption is not satisfied.