IDEAS home Printed from https://ideas.repec.org/a/eee/finlet/v22y2017icp274-279.html
   My bibliography  Save this article

Fast fractional differencing in modeling long memory of conditional variance for high-frequency data

Author

Listed:
  • Klein, Tony
  • Walther, Thomas

Abstract

We transfer the recently introduced fast fractional differencing that utilizes fast Fourier transforms (FFT) to long memory variance models and show that this approach offers immense computation speedups. We demonstrate how calculation times of parameter estimations benefit from this new approach without changing the estimation procedure. A more precise depiction of long memory behavior becomes feasible. The FFT offers a computational advantage to all ARCH(∞)-representations of widely-used long memory models like FIGARCH. Risk management applications like rolling-window Value-at-Risk predictions are substantially sped up. This new approach allows to calculate the conditional volatility of high-frequency in a practicable amount of time.

Suggested Citation

  • Klein, Tony & Walther, Thomas, 2017. "Fast fractional differencing in modeling long memory of conditional variance for high-frequency data," Finance Research Letters, Elsevier, vol. 22(C), pages 274-279.
    • Handle: RePEc:eee:finlet:v:22:y:2017:i:c:p:274-279
    DOI: 10.1016/j.frl.2016.12.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S1544612316304093
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.frl.2016.12.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Christian Conrad & Berthold R. Haag, 2006. "Inequality Constraints in the Fractionally Integrated GARCH Model," Journal of Financial Econometrics, Oxford University Press, vol. 4(3), pages 413-449.
    2. 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.
    3. Mensi, Walid & Hammoudeh, Shawkat & Yoon, Seong-Min, 2014. "Structural breaks and long memory in modeling and forecasting volatility of foreign exchange markets of oil exporters: The importance of scheduled and unscheduled news announcements," International Review of Economics & Finance, Elsevier, vol. 30(C), pages 101-119.
    4. Richard T. Baillie & Young-Wook Han & Robert J. Myers & Jeongseok Song, 2007. "Long Memory and FIGARCH Models for Daily and High Frequency Commodity Prices," Working Papers 594, Queen Mary University of London, School of Economics and Finance.
    5. Richard T. Baillie & Young‐Wook Han & Robert J. Myers & Jeongseok Song, 2007. "Long memory models for daily and high frequency commodity futures returns," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 27(7), pages 643-668, July.
    6. Gourieroux, Christian & Monfort, Alain, 1992. "Qualitative threshold ARCH models," Journal of Econometrics, Elsevier, vol. 52(1-2), pages 159-199.
    7. Andreas Noack Jensen & Morten Ørregaard Nielsen, 2014. "A Fast Fractional Difference Algorithm," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(5), pages 428-436, August.
    8. Muller, Ulrich A. & Dacorogna, Michel M. & Dave, Rakhal D. & Olsen, Richard B. & Pictet, Olivier V. & von Weizsacker, Jacob E., 1997. "Volatilities of different time resolutions -- Analyzing the dynamics of market components," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 213-239, June.
    9. Richard T. Baillie & Young-Wook Han & Robert J. Myers & Jeongseok Song, 2007. "Long Memory and FIGARCH Models for Daily and High Frequency Commodity Prices," Working Papers 594, Queen Mary University of London, School of Economics and Finance.
    10. repec:bla:jecsur:v:16:y:2002:i:3:p:447-85 is not listed on IDEAS
    11. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    12. Li, Muyi & Li, Wai Keung & Li, Guodong, 2015. "A new hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 189(2), pages 428-436.
    13. Brandt, Michael W. & Jones, Christopher S., 2006. "Volatility Forecasting With Range-Based EGARCH Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 470-486, October.
    14. 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.
    15. Baillie, Richard T., 1996. "Long memory processes and fractional integration in econometrics," Journal of Econometrics, Elsevier, vol. 73(1), pages 5-59, July.
    16. Menelaos Karanasos & Zacharias Psaradakis & Martin Sola, 2004. "On the Autocorrelation Properties of Long‐Memory GARCH Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(2), pages 265-282, March.
    17. Tang, Ta-Lun & Shieh, Shwu-Jane, 2006. "Long memory in stock index futures markets: A value-at-risk approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 437-448.
    18. 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.
    19. 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.
    20. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Kawakatsu Hiroyuki, 2021. "Simple Multivariate Conditional Covariance Dynamics Using Hyperbolically Weighted Moving Averages," Journal of Econometric Methods, De Gruyter, vol. 10(1), pages 33-52, January.
    2. Klein, Tony & Pham Thu, Hien & Walther, Thomas, 2018. "Bitcoin is not the New Gold – A comparison of volatility, correlation, and portfolio performance," International Review of Financial Analysis, Elsevier, vol. 59(C), pages 105-116.
    3. Paul Bui Quang & Tony Klein & Nam H. Nguyen & Thomas Walther, 2018. "Value-at-Risk for South-East Asian Stock Markets: Stochastic Volatility vs. GARCH," JRFM, MDPI, vol. 11(2), pages 1-20, April.
    4. Alqahtani, Abdullah & Klein, Tony & Khalid, Ali, 2019. "The impact of oil price uncertainty on GCC stock markets," Resources Policy, Elsevier, vol. 64(C).
    5. Morten Ørregaard Nielsen & Antoine L. Noël, 2020. "To infinity and beyond: Efficient computation of ARCH(\infty) models," Working Paper 1425, Economics Department, Queen's University.
    6. Markus Vogl, 2022. "Quantitative modelling frontiers: a literature review on the evolution in financial and risk modelling after the financial crisis (2008–2019)," SN Business & Economics, Springer, vol. 2(12), pages 1-69, December.
    7. Morten Ørregaard Nielsen & Antoine L. Noël, 2020. "To infinity and beyond: Efficient computation of ARCH(1) models," CREATES Research Papers 2020-13, Department of Economics and Business Economics, Aarhus University.
    8. Walther, Thomas & Klein, Tony & Thu, Hien Pham & Piontek, Krzysztof, 2017. "True or spurious long memory in European non-EMU currencies," Research in International Business and Finance, Elsevier, vol. 40(C), pages 217-230.
    9. Alfeus, Mesias & Nikitopoulos, Christina Sklibosios, 2022. "Forecasting volatility in commodity markets with long-memory models," Journal of Commodity Markets, Elsevier, vol. 28(C).
    10. Morten Ørregaard Nielsen & Antoine L. Noël, 2021. "To infinity and beyond: Efficient computation of ARCH(∞) models," Journal of Time Series Analysis, Wiley Blackwell, vol. 42(3), pages 338-354, May.
    11. Klein, Tony, 2017. "Dynamic correlation of precious metals and flight-to-quality in developed markets," Finance Research Letters, Elsevier, vol. 23(C), pages 283-290.

    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. CHIA-LIN CHANG & MICHAEL McALEER & ROENGCHAI TANSUCHAT, 2012. "Modelling Long Memory Volatility In Agricultural Commodity Futures Returns," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 7(02), pages 1-27.
    2. Onder Buberkoku, 2018. "Examining the Value-at-risk Performance of Fractionally Integrated GARCH Models: Evidence from Energy Commodities," International Journal of Economics and Financial Issues, Econjournals, vol. 8(3), pages 36-50.
    3. Carl Lönnbark, 2016. "Asymmetry with respect to the memory in stock market volatilities," Empirical Economics, Springer, vol. 50(4), pages 1409-1419, June.
    4. Morten Ørregaard Nielsen & Antoine L. Noël, 2020. "To infinity and beyond: Efficient computation of ARCH(1) models," CREATES Research Papers 2020-13, Department of Economics and Business Economics, Aarhus University.
    5. Anagnostidis, Panagiotis & Emmanouilides, Christos J., 2015. "Nonlinearity in high-frequency stock returns: Evidence from the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 421(C), pages 473-487.
    6. Charfeddine, Lanouar, 2016. "Breaks or long range dependence in the energy futures volatility: Out-of-sample forecasting and VaR analysis," Economic Modelling, Elsevier, vol. 53(C), pages 354-374.
    7. Chkili, Walid & Hammoudeh, Shawkat & Nguyen, Duc Khuong, 2014. "Volatility forecasting and risk management for commodity markets in the presence of asymmetry and long memory," Energy Economics, Elsevier, vol. 41(C), pages 1-18.
    8. Tim Bollerslev, 2008. "Glossary to ARCH (GARCH)," CREATES Research Papers 2008-49, Department of Economics and Business Economics, Aarhus University.
    9. Stavroyiannis, S. & Makris, I. & Nikolaidis, V. & Zarangas, L., 2012. "Econometric modeling and value-at-risk using the Pearson type-IV distribution," International Review of Financial Analysis, Elsevier, vol. 22(C), pages 10-17.
    10. Adnen Ben Nasr & Ahdi Noomen Ajmi & Rangan Gupta, 2014. "Modelling the volatility of the Dow Jones Islamic Market World Index using a fractionally integrated time-varying GARCH (FITVGARCH) model," Applied Financial Economics, Taylor & Francis Journals, vol. 24(14), pages 993-1004, July.
    11. Dark, Jonathan, 2018. "Multivariate models with long memory dependence in conditional correlation and volatility," Journal of Empirical Finance, Elsevier, vol. 48(C), pages 162-180.
    12. Toktam Valizadeh & Saeid Rezakhah & Ferdous Mohammadi Basatini, 2021. "On time‐varying amplitude HGARCH model," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 26(2), pages 2538-2547, April.
    13. repec:awi:wpaper:0472 is not listed on IDEAS
    14. Harry Vander Elst, 2015. "FloGARCH : Realizing long memory and asymmetries in returns volatility," Working Paper Research 280, National Bank of Belgium.
    15. González-Pla, Francisco & Lovreta, Lidija, 2019. "Persistence in firm’s asset and equity volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 535(C).
    16. Conrad, Christian, 2010. "Non-negativity conditions for the hyperbolic GARCH model," Journal of Econometrics, Elsevier, vol. 157(2), pages 441-457, August.
    17. Pan, Qunxing & Li, Peng & Du, Xiuli, 2023. "An improved FIGARCH model with the fractional differencing operator (1-νL)d," Finance Research Letters, Elsevier, vol. 55(PB).
    18. Morten Ørregaard Nielsen & Antoine L. Noël, 2020. "To infinity and beyond: Efficient computation of ARCH(\infty) models," Working Paper 1425, Economics Department, Queen's University.
    19. Tomasz Wójtowicz & Henryk Gurgul, 2009. "Long memory of volatility measures in time series," Operations Research and Decisions, Wroclaw University of Science and Technology, Faculty of Management, vol. 19(1), pages 37-54.
    20. Klein, Tony & Walther, Thomas, 2016. "Oil price volatility forecast with mixture memory GARCH," Energy Economics, Elsevier, vol. 58(C), pages 46-58.
    21. repec:ipg:wpaper:2013-009 is not listed on IDEAS
    22. Malinda & Maya & Jo-Hui & Chen, 2022. "Testing for the Long Memory and Multiple Structural Breaks in Consumer ETFs," Journal of Applied Finance & Banking, SCIENPRESS Ltd, vol. 12(6), pages 1-6.

    More about this item

    Keywords

    Computation time; Fractional integration; Fourier transforms; GARCH; Long memory; High-frequency data;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics

    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:eee:finlet:v:22:y:2017:i:c:p:274-279. 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: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/locate/frl .

    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.