Constrained Gamma-Gaussian Mixtures for Modeling Asset Returns

Summary

This paper presents a constrained mixture model for describing asset returns and distinguishing positive, negative, and ranging price behavior. It combines Gamma and Gaussian distributions to represent return patterns while accommodating heavy tails and high kurtosis, features that can make simple distributional assumptions inadequate for financial data.

The model is estimated using the Expectation-Maximisation framework, and the selection of model order is also required to respect the constraints. This offers a structured way to fit a return distribution while preserving the intended interpretation of its components. The excerpt describes the model’s design and estimation approach, but provides no empirical dataset, comparative results, or trading-performance evidence. Its usefulness for strategy selection or forecasting therefore cannot be assessed from the information given.

Key ideas

• The model uses a constrained mixture of Gamma and Gaussian distributions to represent asset returns.
• Its components are intended to distinguish positive, negative, and ranging price behavior.
• The mixture is designed to account for heavy tails and high kurtosis.
• Parameter estimation uses the Expectation-Maximisation framework.
• Model order selection must preserve the model’s constraints.

Tags

# Constrained Mixture Models for Asset Returns Modelling


# Constrained Mixture Models for Asset Returns Modelling









The estimation of asset return distributions is crucial for determining optimal trading strategies. In this paper we describe the constrained mixture model, based on a mixture of Gamma and Gaussian distributions, to provide an accurate description of price trends as being clearly positive, negative or ranging while accounting for heavy tails and high kurtosis. The model is estimated in the Expectation Maximisation framework and model order estimation also respects the model's constraints.

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