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Analytical Derivates of the APARCH Model

Author

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  • Sébastien Laurent

    (CeReFim (Université de Namur), 8 rempart de la vièrge, B5000 Namur, Belgium)

Abstract

This paper derives analytical expressions for the score of the APARCH model of Ding et al. (1993). Interestingly, doing so we derive the analytical score of a broad range of GARCH model since the APARCH model nests at least seven specifications. The use of the APARCH model is now widespread in the literature. However, all the existing applications rely on numerical techniques to calculate the gradients. The paper shows that analytical gradients highly speed-up maximum-likelihood estimation.

Suggested Citation

  • Sébastien Laurent, 2004. "Analytical Derivates of the APARCH Model," Computational Economics, Springer;Society for Computational Economics, vol. 24(1), pages 51-57, August.
    • Handle: RePEc:kap:compec:v:24:y:2004:i:1:p:51-57
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    Cited by:

    1. Stavros Degiannakis & George Filis & Renatas Kizys, 2014. "The Effects of Oil Price Shocks on Stock Market Volatility: Evidence from European Data," The Energy Journal, , vol. 35(1), pages 35-56, January.
    2. Vacca, Gianmarco & Zoia, Maria Grazia & Bagnato, Luca, 2022. "Forecasting in GARCH models with polynomially modified innovations," International Journal of Forecasting, Elsevier, vol. 38(1), pages 117-141.
    3. Amélie Charles & Olivier Darné, 2019. "The accuracy of asymmetric GARCH model estimation," International Economics, CEPII research center, issue 157, pages 179-202.
    4. Tak Siu & John Lau & Hailiang Yang, 2007. "On Valuing Participating Life Insurance Contracts with Conditional Heteroscedasticity," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 14(3), pages 255-275, September.
    5. Hartwell, Christopher A., 2018. "The impact of institutional volatility on financial volatility in transition economies," Journal of Comparative Economics, Elsevier, vol. 46(2), pages 598-615.
    6. Helen Higgs & Andrew C. Worthington, 2005. "Systematic Features of High-Frequency Volatility in Australian Electricity Markets: Intraday Patterns, Information Arrival and Calendar Effects," The Energy Journal, International Association for Energy Economics, vol. 0(Number 4), pages 23-42.
    7. Loi, Tian Sheng Allan & Ng, Jia Le, 2018. "Anticipating electricity prices for future needs – Implications for liberalised retail markets," Applied Energy, Elsevier, vol. 212(C), pages 244-264.
    8. Liu, Yan & Luger, Richard, 2009. "Efficient estimation of copula-GARCH models," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2284-2297, April.
    9. Lambert, Philippe & Laurent, Sébastien & Veredas, David, 2012. "Testing conditional asymmetry: A residual-based approach," Journal of Economic Dynamics and Control, Elsevier, vol. 36(8), pages 1229-1247.
    10. Výrost, Tomáš & Baumöhl, Eduard, 2009. "Asymmetric GARCH and the financial crisis: a preliminary study," MPRA Paper 27909, University Library of Munich, Germany.
    11. K. Diamantopoulos & I. Vrontos, 2010. "A Student-t Full Factor Multivariate GARCH Model," Computational Economics, Springer;Society for Computational Economics, vol. 35(1), pages 63-83, January.
    12. Samet Gunay & Audil Rashid Khaki, 2018. "Best Fitting Fat Tail Distribution for the Volatilities of Energy Futures: Gev, Gat and Stable Distributions in GARCH and APARCH Models," JRFM, MDPI, vol. 11(2), pages 1-19, June.
    13. Vikash Gautam & Vikash Vaibhav, 2017. "Investment, Uncertainty and Credit Market Imperfection in India," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 15(2), pages 265-289, June.
    14. Alex Huang, 2011. "Volatility Modeling by Asymmetrical Quadratic Effect with Diminishing Marginal Impact," Computational Economics, Springer;Society for Computational Economics, vol. 37(3), pages 301-330, March.

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