Loss-based Bayesian Sequential Prediction of Value at Risk with a Long-Memory and Non-linear Realized Volatility Model

TL;DR

This paper introduces RNN-HAR, a novel long-memory, non-linear volatility model for improved Value at Risk forecasting, combining HAR and RNN, with Bayesian inference for sequential prediction, outperforming traditional models.

Contribution

The paper develops RNN-HAR, integrating RNN with HAR for better capturing non-linear and long-memory features in volatility for VaR prediction, using Bayesian inference with SMC.

Findings

RNN-HAR outperforms basic HAR and its extensions in VaR forecasting.

The model effectively captures long-memory and non-linear dynamics.

Empirical results show consistent improvement across 31 market indices.

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.