Quantifying neural network uncertainty under volatility clustering

ArXiv ID: 2402.14476 “View on arXiv”

Authors: Unknown

Abstract

Time-series with volatility clustering pose a unique challenge to uncertainty quantification (UQ) for returns forecasts. Methods for UQ such as Deep Evidential regression offer a simple way of quantifying return forecast uncertainty without the costs of a full Bayesian treatment. However, the Normal-Inverse-Gamma (NIG) prior adopted by Deep Evidential regression is prone to miscalibration as the NIG prior is assigned to latent mean and variance parameters in a hierarchical structure. Moreover, it also overparameterizes the marginal data distribution. These limitations may affect the accurate delineation of epistemic (model) and aleatoric (data) uncertainties. We propose a Scale Mixture Distribution as a simpler alternative which can provide favorable complexity-accuracy trade-off and assign separate subnetworks to each model parameter. To illustrate the performance of our proposed method, we apply it to two sets of financial time-series exhibiting volatility clustering: cryptocurrencies and U.S. equities and test the performance in some ablation studies.

Keywords: Uncertainty Quantification, Volatility Clustering, Deep Evidential Regression, Bayesian Inference, Time Series Forecasting

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.0/10
• Quadrant: Holy Grail
• Why: The paper introduces a novel Scale Mixture Distribution for uncertainty quantification, involving advanced hierarchical probability theory and the interplay between aleatoric and epistemic uncertainties (high math). It validates the method with concrete backtests on financial datasets (cryptocurrencies and U.S. equities) and performs ablation studies, demonstrating implementation-heavy empirical rigor.

  flowchart TD
    A["Research Goal:<br>Quantify Neural Network<br>Uncertainty under<br>Volatility Clustering"] --> B{"Identify Limitations<br>of Deep Evidential Regression"}
    B --> C["Proposed Method:<br>Scale Mixture Distribution"]
    C --> D["Data & Experiments:<br>Cryptos & US Equities<br>+ Ablation Studies"]
    D --> E["Computational Process:<br>Separate Subnetworks for<br>Model Parameters"]
    E --> F["Key Findings:<br>Favorable Complexity-Accuracy<br>Trade-off & Better UQ"]