Paper: arXiv 2408.13588

Authors: Rangika Peiris, Minh-Ngoc Tran, Chao Wang, Richard Gerlach

Abstract

A long memory and non-linear realized volatility model class is proposed for direct Value at Risk (VaR) forecasting. This model, referred to as RNN-HAR, extends the heterogeneous autoregressive (HAR) model, a framework known for efficiently capturing long memory in realized measures, by integrating a Recurrent Neural Network (RNN) to handle non-linear dynamics. Loss-based generalized Bayesian inference with Sequential Monte Carlo is employed for model estimation and sequential prediction in RNN HAR. The empirical analysis is conducted using daily closing prices and realized measures from 2000 to 2022 across 31 market indices. The proposed models one step ahead VaR forecasting performance is compared against a basic HAR model and its extensions. The results demonstrate that the proposed RNN-HAR model consistently outperforms all other models considered in the study.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents an innovative hybrid framework combining recurrent neural networks with the classical HAR model, leveraging generalized loss-based Bayesian inference and SMC. Its empirical section is highly rigorous, featuring extensive one-step-ahead VaR backtesting across 31 global equity market indices spanning over two decades.

Research Flowchart

  flowchart TD
    A[<b>Research Goal:</b><br>Improve 1-step-ahead Value at Risk prediction via long-memory & non-linear modeling] --> B[<b>Data Input:</b><br>Daily prices & realized measures for 31 market indices]
    B --> C[<b>Model Formulation:</b><br>RNN-HAR Model<br><i>Combines HAR long-memory with RNN non-linearity</i>]
    C --> D[<b>Estimation & Prediction:</b><br>Loss-based Generalized Bayesian Inference via Sequential Monte Carlo]
    D --> E[<b>Comparative Analysis:</b><br>Evaluate against benchmark HAR and extension models]
    E --> F[<b>Key Outcome:</b><br>RNN-HAR consistently outperforms all benchmarks in VaR forecasting accuracy]

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