Experiments on the application of IOHMMs to model financial returns series

Area of Science:

• Machine Learning
• Financial Econometrics
• Time Series Analysis

Background:

• Hidden Markov Models (HMMs) are foundational for sequence modeling.
• Input-Output Hidden Markov Models (IOHMMs) extend HMMs by incorporating input sequences to condition probability distributions.
• Financial time-series analysis requires sophisticated models to capture complex dependencies.

Purpose of the Study:

• To compare the generalization performance of various IOHMMs and related models on financial time-series prediction.
• To evaluate model accuracy in predicting conditional densities of market and sector index returns.
• To determine the effectiveness of IOHMMs for capturing higher moments in financial data.

Main Methods:

• Implemented and compared several models: unconditional Gaussian, conditional linear Gaussian, Gaussian mixtures, HMMs, and various IOHMMs.
• Utilized financial time-series data, specifically market and sector index returns.
• Assessed model performance using out-of-sample likelihood to estimate prediction accuracy.

Main Results:

• The historical average provided the best results for estimating the first moment (mean) of returns.
• IOHMMs demonstrated significantly superior performance for predicting higher moments of the return distribution.
• Out-of-sample likelihood indicated a clear advantage for IOHMMs in capturing complex financial dynamics.

Conclusions:

• IOHMMs are highly effective for financial time-series prediction, particularly for higher-order moments.
• The choice of model significantly impacts prediction accuracy, with IOHMMs offering advanced capabilities.
• Future research can explore diverse conditional distributions within IOHMMs for enhanced financial modeling.