Forecasting High Dimensional Volatility Using Conditional Restricted Boltzmann Machine on GPU

Forecasting the volatility of multivariate asset return is an important issue in financial econometric analysis, where the volatility is represented by a conditional covariance matrix (CCM). Traditional models for predicting CCM such as GARCH(1, 1) models are not capable of dealing with high-dimensional case for there are N(N+1)/2 necessary entries in the CCM of N-variant asset return. We propose an approach for forecasting the high-dimensional CCM by using Conditional Restricted Boltzmann Machine (CRBM), which is a recently proposed machine learning tools for modeling time series and has a high degree of parallelization. In this study, we construct a CRBM to model high-dimensional time-varying CCM and accelerate the computation of CRBM by making heavy use of CUBLAS on GPU. Our experimental results show speedups of over 70 times for high-dimensional case compared to the sequential implementation and over 140 times compared to traditional GARCH(1, 1) models without loss of forecasting accuracy.