No Cover Image

Journal article 284 views

The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns* / Yuzhi Cai; Julian Stander

Journal of Financial Econometrics, Volume: 18, Issue: 2, Pages: 395 - 424

Swansea University Author: Yuzhi, Cai

  • Accepted Manuscript under embargo until: 3rd May 2021

Check full text

DOI (Published version): 10.1093/jjfinec/nbz014

Abstract

We consider multiple threshold value-at-risk (VaR\(_t\)) estimation and density forecasting for financial data following a threshold GARCH model. We develop an \(\alpha\)-quantile quasi-maximum likelihood estimation (QMLE) method for VaR\(_t\) by showing that the associated density function is an \(...

Full description

Published in: Journal of Financial Econometrics
ISSN: 1479-8409 1479-8417
Published: Oxford University Press (OUP) 2019
Online Access: Check full text

URI: https://cronfa.swan.ac.uk/Record/cronfa49769
Tags: Add Tag
No Tags, Be the first to tag this record!
Abstract: We consider multiple threshold value-at-risk (VaR\(_t\)) estimation and density forecasting for financial data following a threshold GARCH model. We develop an \(\alpha\)-quantile quasi-maximum likelihood estimation (QMLE) method for VaR\(_t\) by showing that the associated density function is an \(\alpha\)-quantile density and belongs to the tick-exponential family. This establishes that our estimator is consistent for the parameters of VaR\(_t\). We propose a density forecasting method for quantile models based on VaR\(_t\) at a single non-extreme level, which overcomes some limitations of existing forecasting methods with quantile models. We find that for heavy-tailed financial data our \(\alpha\)-quantile QMLE method for VaR\(_t\) outperms the Gaussian QMLE method for volatility. We also find that density forecasts based on VaR\(_t\) outperform those based on the volatility of financial data. Empirical work on market returns shows that our approach also outperforms some benchmark models for density forecasting of financial returns.
Keywords: \(\alpha\)-quantile density, density forecasting, QMLE, threshold, value-at-risk (VaR)
College: School of Management
Issue: 2
Start Page: 395
End Page: 424