Wavelet-stochastic-chaos informed machine learning framework for multivariate financial time-series prediction

Abstract

Financial time series forecasting poses significant challenges due to the diverse risk profiles and dynamic behaviors of assets such as the S&P 500, NASDAQ, and Bitcoin, especially across different market periods. This study introduces a novel framework, waveletstochastic-chaos informed machine learning, that integrates wavelet transforms, stochastic processes, and chaos theory to improve machine learning prediction accuracy over a decade (2015–2025). The analysis is divided into four distinct periods: All Time, PreCOVID, COVID, and Post-COVID. The aim is to capture the multi-scale patterns, volatility, and complexity inherent in financial data, which will be assessed across various market conditions. The framework outperforms the baseline maximum likelihood models in most scenarios, achieving significant root mean squared errors for the scaled price predictions of S&P 500 (e.g., from 0.0348 to 0.0122 in All Time), NASDAQ (e.g., from 0.0284 to 0.0180 in All Time) and Bitcoin (e.g., from 0.0838 to 0.0288 in All Time) based on 1000 experimental trials. It excels in volatile periods like COVID and for high-risk Bitcoin, though it slightly underperforms in the stable Post-COVID recovery for S&P 500. Wavelet features are found to be critical for accuracy. Additionally, stochastic and chaos-based elements enhance performance in volatile and complex contexts, respectively, as confirmed by ablation studies. This study provides empirical evidence of predictive utility for financial time-series forecasting in assets with different dynamics and market regimes. The results indicate that multi-scale, stochastic, and complexity-based feature representations can improve forecasting performance within the examined datasets, suggesting that the framework may apply to other non-stationary time-series settings, although such extensions remain for future investigation.

Keywords

• Chaos theory
• financial time series
• machine learning
• stochastic process
• wavelets

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