Fundamentals of matrix computations
Fundamentals of matrix computations
Information processing in dynamical systems: foundations of harmony theory
Parallel distributed processing: explorations in the microstructure of cognition, vol. 1
Training products of experts by minimizing contrastive divergence
Neural Computation
Forecasting volatility based on wavelet support vector machine
Expert Systems with Applications: An International Journal
Two Distributed-State Models For Generating High-Dimensional Time Series
The Journal of Machine Learning Research
The influence of ARIMA-GARCH parameters in feed forward neural networks prediction
Neural Computing and Applications - Special Issue on WCCI2008
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Forecasting volatility is an important issue in financial econometric analysis. This paper aims to seek a computationally feasible approach for predicting large scale conditional volatility and covariance of financial time series. In the case of multi-variant time series, the volatility is represented by a Conditional Covariance Matrix (CCM). Traditional models for predicting CCM such as GARCH models are incapable of dealing with high-dimensional cases as there are O(N 2) parameters to be estimated in the case of N-variant asset return, and it is difficult to accelerate the computation of estimating these parameters by utilizing modern multi-core architecture. These GARCH models also have difficulties in modeling non-linear properties. The widely used Restricted Boltzmann Machine (RBM) is an energy-based stochastic recurrent neural network and its extended model, Conditional RBM (CRBM), has shown its capability in modeling high-dimensional time series. In this paper, we first propose a CRBM-based approach to forecast CCM and show how to capture the long memory properties in volatility, and then we implement the proposed model on GPU by using CUDA and CUBLAS. Experiment results indicate that the proposed CRBM-based model obtains better forecasting accuracy for low-dimensional volatility and it also shows great potential in modeling for large-scale cases compared with traditional GARCH models.