IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2609.06422.html

Asymmetric Long-Memory GARCH: Sign-Dependent Kernel Injection in a Two-Dimensional Markov Chain

Author

Listed:
  • Kennedy Titus Kayaki
  • Kyungsub Lee

Abstract

We introduce ALM-GARCH, an asymmetric long-memory GARCH model in which positive and negative innovations enter conditional variance with different injection amplitudes and kernel offsets. These departures define testable level and memory channels relative to a nested symmetric benchmark. Positive Harris recurrence holds for interior configurations under a Foster-Lyapunov condition. Across five equity indices and Bitcoin, joint symmetry is rejected throughout, driven primarily by the level channel. The memory channel is supported for the Nikkei 225, KOSPI, and Bitcoin but is weakly identified when the positive branch is nearly inactive. Out-of-sample performance is broadly comparable to standard benchmarks.

Suggested Citation

  • Kennedy Titus Kayaki & Kyungsub Lee, 2026. "Asymmetric Long-Memory GARCH: Sign-Dependent Kernel Injection in a Two-Dimensional Markov Chain," Papers 2609.06422, arXiv.org.
    • Handle: RePEc:arx:papers:2609.06422
    as

    Download full text from publisher

    File URL: https://arxiv.org/pdf/2609.06422
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    2. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    3. Andrews, Donald W K, 2001. "Testing When a Parameter Is on the Boundary of the Maintained Hypothesis," Econometrica, Econometric Society, vol. 69(3), pages 683-734, May.
    4. Fulvio Corsi, 2009. "A Simple Approximate Long-Memory Model of Realized Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 7(2), pages 174-196, Spring.
    5. Baillie, Richard T. & Bollerslev, Tim & Mikkelsen, Hans Ole, 1996. "Fractionally integrated generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 74(1), pages 3-30, September.
    6. Ding, Zhuanxin & Granger, Clive W. J. & Engle, Robert F., 1993. "A long memory property of stock market returns and a new model," Journal of Empirical Finance, Elsevier, vol. 1(1), pages 83-106, June.
    7. Bollerslev, Tim & Ole Mikkelsen, Hans, 1996. "Modeling and pricing long memory in stock market volatility," Journal of Econometrics, Elsevier, vol. 73(1), pages 151-184, July.
    8. Markus Haas, 2004. "A New Approach to Markov-Switching GARCH Models," Journal of Financial Econometrics, Oxford University Press, vol. 2(4), pages 493-530.
    9. Andersen, Torben G & Bollerslev, Tim, 1998. "Answering the Skeptics: Yes, Standard Volatility Models Do Provide Accurate Forecasts," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 885-905, November.
    10. Diebold, Francis X & Mariano, Roberto S, 2002. "Comparing Predictive Accuracy," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(1), pages 134-144, January.
    11. Kyungsub Lee & Kennedy Titus Kayaki, 2026. "Long-memory GARCH via a two-dimensional Markov chain," Papers 2607.25189, arXiv.org.
    12. Glosten, Lawrence R & Jagannathan, Ravi & Runkle, David E, 1993. "On the Relation between the Expected Value and the Volatility of the Nominal Excess Return on Stocks," Journal of Finance, American Finance Association, vol. 48(5), pages 1779-1801, December.
    13. Y. K. Tse, 1998. "The conditional heteroscedasticity of the yen-dollar exchange rate," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 13(1), pages 49-55.
    14. Patton, Andrew J., 2011. "Volatility forecast comparison using imperfect volatility proxies," Journal of Econometrics, Elsevier, vol. 160(1), pages 246-256, January.
    15. Davidson, James, 2004. "Moment and Memory Properties of Linear Conditional Heteroscedasticity Models, and a New Model," Journal of Business & Economic Statistics, American Statistical Association, vol. 22(1), pages 16-29, January.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Ma, Feng & Li, Yu & Liu, Li & Zhang, Yaojie, 2018. "Are low-frequency data really uninformative? A forecasting combination perspective," The North American Journal of Economics and Finance, Elsevier, vol. 44(C), pages 92-108.
    2. Mehmet Sahiner, 2022. "Forecasting volatility in Asian financial markets: evidence from recursive and rolling window methods," SN Business & Economics, Springer, vol. 2(10), pages 1-74, October.
    3. Halkos, George E. & Tsirivis, Apostolos S., 2019. "Effective energy commodity risk management: Econometric modeling of price volatility," Economic Analysis and Policy, Elsevier, vol. 63(C), pages 234-250.
    4. Nikolaos A. Kyriazis, 2021. "A Survey on Volatility Fluctuations in the Decentralized Cryptocurrency Financial Assets," JRFM, MDPI, vol. 14(7), pages 1-46, June.
    5. Liu, Li & Wan, Jieqiu, 2012. "A study of Shanghai fuel oil futures price volatility based on high frequency data: Long-range dependence, modeling and forecasting," Economic Modelling, Elsevier, vol. 29(6), pages 2245-2253.
    6. Harry-Paul Vander Elst, 2015. "FloGARCH: Realizing Long Memory and Asymmetries in Returns Valitility," Working Papers ECARES ECARES 2015-12, ULB -- Universite Libre de Bruxelles.
    7. Kyungsub Lee & Kennedy Titus Kayaki, 2026. "Long-memory GARCH via a two-dimensional Markov chain," Papers 2607.25189, arXiv.org.
    8. Trino-Manuel Ñíguez, 2008. "Volatility and VaR forecasting in the Madrid Stock Exchange," Spanish Economic Review, Springer;Spanish Economic Association, vol. 10(3), pages 169-196, September.
    9. repec:awi:wpaper:0472 is not listed on IDEAS
    10. Ma, Feng & Wei, Yu & Huang, Dengshi & Chen, Yixiang, 2014. "Which is the better forecasting model? A comparison between HAR-RV and multifractality volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 171-180.
    11. N. Antonakakis & J. Darby, 2013. "Forecasting volatility in developing countries' nominal exchange returns," Applied Financial Economics, Taylor & Francis Journals, vol. 23(21), pages 1675-1691, November.
    12. Wen Cheong Chin & Min Cherng Lee, 2018. "S&P500 volatility analysis using high-frequency multipower variation volatility proxies," Empirical Economics, Springer, vol. 54(3), pages 1297-1318, May.
    13. Hou, Aijun & Suardi, Sandy, 2012. "A nonparametric GARCH model of crude oil price return volatility," Energy Economics, Elsevier, vol. 34(2), pages 618-626.
    14. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, June.
    15. Sébastien Laurent & Jeroen V. K. Rombouts & Francesco Violante, 2012. "On the forecasting accuracy of multivariate GARCH models," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 27(6), pages 934-955, September.
    16. Dilip Kumar, 2018. "Modeling and Forecasting Unbiased Extreme Value Volatility Estimator in Presence of Leverage Effect," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 16(2), pages 313-335, June.
    17. Olusanya E. Olubusoye & OlaOluwa S. Yaya, 2016. "Time series analysis of volatility in the petroleum pricing markets: the persistence, asymmetry and jumps in the returns series," OPEC Energy Review, Organization of the Petroleum Exporting Countries, vol. 40(3), pages 235-262, September.
    18. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2006. "Volatility and Correlation Forecasting," Handbook of Economic Forecasting, in: G. Elliott & C. Granger & A. Timmermann (ed.), Handbook of Economic Forecasting, edition 1, volume 1, chapter 15, pages 777-878, Elsevier.
    19. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2005. "Volatility forecasting," CFS Working Paper Series 2005/08, Center for Financial Studies (CFS).
    20. Gavriilidis, Konstantinos & Kambouroudis, Dimos S. & Tsakou, Katerina & Tsouknidis, Dimitris A., 2018. "Volatility forecasting across tanker freight rates: The role of oil price shocks," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 118(C), pages 376-391.
    21. Stavros Stavroyiannis, 2017. "A note on the Nelson Cao inequality constraints in the GJR-GARCH model: Is there a leverage effect?," Papers 1705.00535, arXiv.org.

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:arx:papers:2609.06422. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: arXiv administrators (email available below). General contact details of provider: https://arxiv.org/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.