Dynamic Boltzmann Machines for Second Order Moments and Generalized Gaussian Distributions

TL;DR

This paper extends Dynamic Boltzmann Machines to model time-varying variance and generalized Gaussian distributions, improving financial time-series prediction accuracy.

Contribution

The paper introduces an extension of DyBM that captures dynamic variance and heavy-tailed distributions, addressing limitations in modeling financial data.

Findings

Enhanced prediction of financial time-series data.

Significant performance improvements over existing models.

Ability to model heavy-tailed and non-constant variance distributions.

Abstract

Dynamic Boltzmann Machine (DyBM) has been shown highly efficient to predict time-series data. Gaussian DyBM is a DyBM that assumes the predicted data is generated by a Gaussian distribution whose first-order moment (mean) dynamically changes over time but its second-order moment (variance) is fixed. However, in many financial applications, the assumption is quite limiting in two aspects. First, even when the data follows a Gaussian distribution, its variance may change over time. Such variance is also related to important temporal economic indicators such as the market volatility. Second, financial time-series data often requires learning datasets generated by the generalized Gaussian distribution with an additional shape parameter that is important to approximate heavy-tailed distributions. Addressing those aspects, we show how to extend DyBM that results in significant performance improvement in predicting financial time-series data.