Stochastic nonlinear time series forecasting using time-delay reservoir computers: performance and universality.

Area of Science:

• Machine Learning
• Computational Finance
• Time Series Analysis

Background:

• Reservoir computing (RC) is an emerging machine learning approach demonstrating high efficacy in empirical data processing.
• Time-delay reservoirs (TDRs), a specific RC type, are built from time-delay differential equations, offering unique computational properties.

Purpose of the Study:

• To evaluate the performance of TDRs in forecasting conditional covariances for multivariate nonlinear stochastic processes (VEC-GARCH type).
• To assess TDRs' capability in predicting daily market realized volatilities using historical log-return data.
• To address and propose solutions for the limited task-universality of individual reservoirs.

Main Methods:

• Utilized time-delay reservoirs constructed from sampled solutions of time-delay differential equations.
• Employed daily log-return series as training input for forecasting financial market data.
• Developed a solution using parallel arrays of TDRs to overcome individual reservoir limitations.

Main Results:

• Demonstrated strong performance of TDRs in forecasting conditional covariances of VEC-GARCH processes.
• Achieved accurate prediction of daily market realized volatilities computed from intraday quotes.
• Showcased the effectiveness of parallel TDR arrays in enhancing task-universality.

Conclusions:

• Time-delay reservoir computing is a powerful tool for complex financial time series forecasting.
• Parallel TDR architectures offer a viable strategy to improve the adaptability and robustness of reservoir computing models.
• The study highlights the potential of TDRs in quantitative finance and empirical data analysis.