<p>Daily Close Price (<i>CP</i>) prognosis using deep learning models faces distinctive challenges due to two fundamental types of uncertainties, namely aleatoric and epistemic, which remain largely unexplored in existing studies. The former is due to random market conditions, and the latter is due to the model’s limitations in addressing the knowledge gap to interpret complex dynamic <i>CP</i> movement. Traditional machine learning models often fail to address both market dynamics and model limitations simultaneously. This study presents <b>Pr</b>ice<b>Flow</b> (PrFlow): A deep hybrid bidirectional recurrent model with BiLSTM-BiGRU parallel pathways layer, a volatility-adaptive (<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(V_Y\)</EquationSource> </InlineEquation>) framework designed to enhance daily CP prognosis across low-high volatility regimes. The research adopts a dual evaluation approach: (1) a comparative analysis of six standard RNN variants—GRU, LSTM, bidirectional, and attention-based architectures—applied to financial data from 2015 to 2024 across eight sectors; and (2) a systematic assessment of the PrFlow architecture using key performance metrics: root mean square error, mean absolute error, R-square, prediction of change in direction, mean directional accuracy, symmetric mean absolute percentage error, Hurst exponent, and statistical paired <i>t</i> and Wilcoxon rank–sum tests. The results of the proposed model demonstrate improved accuracy (<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(R^2\)</EquationSource> </InlineEquation> up to 0.99), reduced SMAPE by 10%, and robust directional performance (MDA/POCID 45.1–53.6%) compared to state-of-the-art models. The framework proves effective in navigating uncertainties in both limited market historical financial data and reduced model training opportunities, thus offering a reliable tool for financial analysts and investors. This work contributes a <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(V_Y\)</EquationSource> </InlineEquation> aware, uncertainty-resilient forecasting strategy, with potential applications in risk management, portfolio optimization, and automated trading systems.</p>

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Enhancing Aleatoric and Epistemic Uncertainty Prognostication of Financial Data through Volatility-Adaptive Framework

  • Ankush Goyal,
  • Richa Golash,
  • Ajay Kumar

摘要

Daily Close Price (CP) prognosis using deep learning models faces distinctive challenges due to two fundamental types of uncertainties, namely aleatoric and epistemic, which remain largely unexplored in existing studies. The former is due to random market conditions, and the latter is due to the model’s limitations in addressing the knowledge gap to interpret complex dynamic CP movement. Traditional machine learning models often fail to address both market dynamics and model limitations simultaneously. This study presents PriceFlow (PrFlow): A deep hybrid bidirectional recurrent model with BiLSTM-BiGRU parallel pathways layer, a volatility-adaptive ( \(V_Y\) ) framework designed to enhance daily CP prognosis across low-high volatility regimes. The research adopts a dual evaluation approach: (1) a comparative analysis of six standard RNN variants—GRU, LSTM, bidirectional, and attention-based architectures—applied to financial data from 2015 to 2024 across eight sectors; and (2) a systematic assessment of the PrFlow architecture using key performance metrics: root mean square error, mean absolute error, R-square, prediction of change in direction, mean directional accuracy, symmetric mean absolute percentage error, Hurst exponent, and statistical paired t and Wilcoxon rank–sum tests. The results of the proposed model demonstrate improved accuracy ( \(R^2\) up to 0.99), reduced SMAPE by 10%, and robust directional performance (MDA/POCID 45.1–53.6%) compared to state-of-the-art models. The framework proves effective in navigating uncertainties in both limited market historical financial data and reduced model training opportunities, thus offering a reliable tool for financial analysts and investors. This work contributes a \(V_Y\) aware, uncertainty-resilient forecasting strategy, with potential applications in risk management, portfolio optimization, and automated trading systems.