IDEAS home Printed from https://ideas.repec.org/a/prg/jnlaop/v2014y2014i1id423p3-26.html
   My bibliography  Save this article

Simulating Bivariate Stationary Processes with Scale-Specific Characteristics

Author

Listed:
  • Milan Bašta

Abstract

By modifying and generalizing the wavelet-based approach of approximately simulating univariate long-memory processes that is available in the literature, we propose a methodology for simulating a bivariate stationary process, whose components exhibit different relationships at different scales. We derive the formulas for the autocovariance and cross-covariance sequences of the simulated bivariate process. We provide a setting for the parameters of the simulation which might generate a bivariate time series resembling that of stock log returns. Using this setting, we study the properties of our methodology via Monte Carlo simulation.

Suggested Citation

  • Milan Bašta, 2014. "Simulating Bivariate Stationary Processes with Scale-Specific Characteristics," Acta Oeconomica Pragensia, Prague University of Economics and Business, vol. 2014(1), pages 3-26.
    • Handle: RePEc:prg:jnlaop:v:2014:y:2014:i:1:id:423:p:3-26
    DOI: 10.18267/j.aop.423
    as

    Download full text from publisher

    File URL: http://aop.vse.cz/doi/10.18267/j.aop.423.html
    Download Restriction: free of charge
    File URL: http://aop.vse.cz/doi/10.18267/j.aop.423.pdf
    Download Restriction: free of charge
    File URL: https://libkey.io/10.18267/j.aop.423?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. G. P. Nason & R. Von Sachs & G. Kroisandt, 2000. "Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(2), pages 271-292.
    2. 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.
    3. Sanderson, Jean & Fryzlewicz, Piotr & Jones, M. W., 2010. "Estimating linear dependence between nonstationary time series using the locally stationary wavelet model," LSE Research Online Documents on Economics 29141, London School of Economics and Political Science, LSE Library.
    4. Zumbach, Gilles & Lynch, Paul, 2001. "Heterogeneous volatility cascade in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 521-529.
    5. J. Sanderson & P. Fryzlewicz & M. W. Jones, 2010. "Estimating linear dependence between nonstationary time series using the locally stationary wavelet model," Biometrika, Biometrika Trust, vol. 97(2), pages 435-446.
    6. Gilles Zumbach & Paul Lynch, 2001. "Heterogeneous volatility cascade in financial markets," Papers cond-mat/0105162, arXiv.org.
    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. Mark Fiecas & Hernando Ombao, 2016. "Modeling the Evolution of Dynamic Brain Processes During an Associative Learning Experiment," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 111(516), pages 1440-1453, October.
    2. von Sachs, Rainer, 2019. "Spectral Analysis of Multivariate Time Series," LIDAM Discussion Papers ISBA 2019008, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    3. Aykroyd, Robert G. & Barber, Stuart & Miller, Luke R., 2016. "Classification of multiple time signals using localized frequency characteristics applied to industrial process monitoring," Computational Statistics & Data Analysis, Elsevier, vol. 94(C), pages 351-362.
    4. Marcus Cordi & Damien Challet & Serge Kassibrakis, 2021. "The market nanostructure origin of asset price time reversal asymmetry," Quantitative Finance, Taylor & Francis Journals, vol. 21(2), pages 295-304, February.
    5. Cho, Haeran & Fryzlewicz, Piotr, 2015. "Multiple-change-point detection for high dimensional time series via sparsified binary segmentation," LSE Research Online Documents on Economics 57147, London School of Economics and Political Science, LSE Library.
    6. Marcus Cordi & Serge Kassibrakis & Damien Challet, 2018. "The market nanostructure origin of asset price time reversal asymmetry," Working Papers hal-01966419, HAL.
    7. Euan T. McGonigle & Rebecca Killick & Matthew A. Nunes, 2022. "Trend locally stationary wavelet processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 43(6), pages 895-917, November.
    8. Embleton, Jonathan & Knight, Marina I. & Ombao, Hernando, 2022. "Wavelet testing for a replicate-effect within an ordered multiple-trial experiment," Computational Statistics & Data Analysis, Elsevier, vol. 174(C).
    9. Blanc, Pierre & Chicheportiche, Rémy & Bouchaud, Jean-Philippe, 2014. "The fine structure of volatility feedback II: Overnight and intra-day effects," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 402(C), pages 58-75.
    10. Guy Nason, 2013. "A test for second-order stationarity and approximate confidence intervals for localized autocovariances for locally stationary time series," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 75(5), pages 879-904, November.
    11. Gilles Zumbach, 2007. "Time reversal invariance in finance," Papers 0708.4022, arXiv.org.
    12. David Mcmillan & Alan Speight, 2008. "Long-memory in high-frequency exchange rate volatility under temporal aggregation," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 251-261.
    13. Omar El Euch & Jim Gatheral & Radov{s} Radoiv{c}i'c & Mathieu Rosenbaum, 2018. "The Zumbach effect under rough Heston," Papers 1809.02098, arXiv.org.
    14. Ramazan Gencay & Nikola Gradojevic & Faruk Selcuk & Brandon Whitcher, 2010. "Asymmetry of information flow between volatilities across time scales," Quantitative Finance, Taylor & Francis Journals, vol. 10(8), pages 895-915.
    15. Julien Idier, 2011. "Long-term vs. short-term comovements in stock markets: the use of Markov-switching multifractal models," The European Journal of Finance, Taylor & Francis Journals, vol. 17(1), pages 27-48.
    16. Wang, Jiangyan & Cao, Guanqun & Wang, Li & Yang, Lijian, 2020. "Simultaneous confidence band for stationary covariance function of dense functional data," Journal of Multivariate Analysis, Elsevier, vol. 176(C).
    17. Clark, Andrew, 2004. "Evidence of log-periodicity in corporate bond spreads," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 338(3), pages 585-595.
    18. Nicolas Boitout & Loredana Ureche-Rangau, 2004. "Towards A Multifractal Paradigm Of Stochastic Volatility?," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(07), pages 823-851.
    19. Wang, Xunxiao & Wu, Chongfeng & Xu, Weidong, 2015. "Volatility forecasting: The role of lunch-break returns, overnight returns, trading volume and leverage effects," International Journal of Forecasting, Elsevier, vol. 31(3), pages 609-619.
    20. Gilles Zumbach, 2010. "Volatility conditional on price trends," Quantitative Finance, Taylor & Francis Journals, vol. 10(4), pages 431-442.

    More about this item

    Keywords

    time series; bivariate; wavelets; finance;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C49 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Other
    • C53 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Forecasting and Prediction Models; Simulation Methods
    • C58 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Financial Econometrics
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)

    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:prg:jnlaop:v:2014:y:2014:i:1:id:423:p:3-26. 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: Stanislav Vojir (email available below). General contact details of provider: https://edirc.repec.org/data/uevsecz.html .

    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.