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The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*

Yuzhi Cai Orcid Logo, Julian Stander

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

Swansea University Author: Yuzhi Cai Orcid Logo

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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 \(...

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Published in: Journal of Financial Econometrics
ISSN: 1479-8409 1479-8417
Published: Oxford University Press (OUP) 2019
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URI: https://cronfa.swan.ac.uk/Record/cronfa49769
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spelling 2021-01-25T16:23:33.3515581 v2 49769 2019-03-27 The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns* eff7b8626ab4cc6428eef52516fda7d6 0000-0003-3509-9787 Yuzhi Cai Yuzhi Cai true false 2019-03-27 BAF 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. Journal Article Journal of Financial Econometrics 18 2 395 424 Oxford University Press (OUP) 1479-8409 1479-8417 \(\alpha\)-quantile density, density forecasting, QMLE, threshold, value-at-risk (VaR) 31 12 2019 2019-12-31 10.1093/jjfinec/nbz014 COLLEGE NANME Accounting and Finance COLLEGE CODE BAF Swansea University 2021-01-25T16:23:33.3515581 2019-03-27T09:30:44.8994084 School of Management Accounting and Finance Yuzhi Cai 0000-0003-3509-9787 1 Julian Stander 2 0049769-27032019121328.pdf bayesian_tgarch-b.pdf 2019-03-27T12:13:28.9400000 Output 939602 application/pdf Accepted Manuscript true 2021-05-03T00:00:00.0000000 true eng
title The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
spellingShingle The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
Yuzhi Cai
title_short The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
title_full The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
title_fullStr The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
title_full_unstemmed The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
title_sort The Threshold GARCH Model: Estimation and Density Forecasting for Financial Returns*
author_id_str_mv eff7b8626ab4cc6428eef52516fda7d6
author_id_fullname_str_mv eff7b8626ab4cc6428eef52516fda7d6_***_Yuzhi Cai
author Yuzhi Cai
author2 Yuzhi Cai
Julian Stander
format Journal article
container_title Journal of Financial Econometrics
container_volume 18
container_issue 2
container_start_page 395
publishDate 2019
institution Swansea University
issn 1479-8409
1479-8417
doi_str_mv 10.1093/jjfinec/nbz014
publisher Oxford University Press (OUP)
college_str School of Management
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hierarchy_top_title School of Management
hierarchy_parent_id schoolofmanagement
hierarchy_parent_title School of Management
department_str Accounting and Finance{{{_:::_}}}School of Management{{{_:::_}}}Accounting and Finance
document_store_str 1
active_str 0
description 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.
published_date 2019-12-31T04:18:24Z
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