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Value at Risk forecasting with the ARMA-GARCH family of models in times of increased volatility

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Abstract

The paper evaluates several hundred one-day-ahead VaR forecasting models in the time period between the years 2004 and 2009 on data from six world stock indices - DJI, GSPC, IXIC, FTSE, GDAXI and N225. The models model mean using the ARMA processes with up to two lags and variance with one of GARCH, EGARCH or TARCH processes with up to two lags. The models are estimated on the data from the in-sample period and their forecasting accuracy is evaluated on the out-of-sample data, which are more volatile. The main aim of the paper is to test whether a model estimated on data with lower volatility can be used in periods with higher volatility. The evaluation is based on the conditional coverage test and is performed on each stock index separately. The primary result of the paper is that the volatility is best modelled using a GARCH process and that an ARMA process pattern cannot be found in analyzed time series.

Suggested Citation

  • Milan Rippel & Ivo Jánský, 2011. "Value at Risk forecasting with the ARMA-GARCH family of models in times of increased volatility," Working Papers IES 2011/27, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, revised Jul 2011.
    • Handle: RePEc:fau:wpaper:wp2011_27
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    File URL: http://ies.fsv.cuni.cz/default/file/download/id/17146
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    Cited by:

    1. Eyden Samunderu & Yvonne T. Murahwa, 2021. "Return Based Risk Measures for Non-Normally Distributed Returns: An Alternative Modelling Approach," JRFM, MDPI, vol. 14(11), pages 1-48, November.
    2. Tomas Adam & Sona Benecka & Ivo Jansky, 2012. "Time-Varying Betas of Banking Sectors," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 62(6), pages 485-504, December.
    3. Wang, Xiaoyu & Xie, Dejun & Jiang, Jingjing & Wu, Xiaoxia & He, Jia, 2017. "Value-at-Risk estimation with stochastic interest rate models for option-bond portfolios," Finance Research Letters, Elsevier, vol. 21(C), pages 10-20.
    4. Timmy Elenjical & Patrick Mwangi & Barry Panulo & Chun-Sung Huang, 2016. "A comparative cross-regime analysis on the performance of GARCH-based value-at-risk models: Evidence from the Johannesburg stock exchange," Risk Management, Palgrave Macmillan, vol. 18(2), pages 89-110, August.
    5. Chhorn, Theara & Chaiboonsri, Chukiat, 2017. "Modelling and Forecasting Tourist Arrivals to Cambodia: An Application of ARIMA-GARCH Approach," MPRA Paper 83942, University Library of Munich, Germany, revised 27 Dec 2017.
    6. Tomáš Konderla & Václav Klepáč, 2017. "Using HMM Approach for Assessing Quality of Value at Risk Estimation: Evidence from PSE Listed Company," Acta Universitatis Agriculturae et Silviculturae Mendelianae Brunensis, Mendel University Press, vol. 65(5), pages 1687-1694.

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    More about this item

    Keywords

    VaR; risk analysis; conditional volatility; conditional coverage; garch; egarch; tarch; moving average process; autoregressive process;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G01 - Financial Economics - - General - - - Financial Crises
    • G24 - Financial Economics - - Financial Institutions and Services - - - Investment Banking; Venture Capital; Brokerage

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