IDEAS home Printed from https://ideas.repec.org/p/wuu/wpaper/hsc1104.html
   My bibliography  Save this paper

Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution

Author

Listed:
  • Agnieszka Wylomanska

Abstract

In this paper we investigate the dependence structure for Ornstein–Uhlenbeck process with tempered stable distribution that is natural extension of the classical Ornstein–Uhlenbeck process with Gaussian and alpha-stable behavior. However, for the alpha-stable models the correlation is not defined, therefore in order to compare the structure of dependence for Ornstein–Uhlenbeck process with tempered stable and alpha-stable distribution, we need another measures of dependence defined for infinitely divisible processes such as Levy correlation cascade or codifference. We show that for analyzed tempered stable process the rate of decay of the Levy correlation cascade is different than in the stable case, while the codifference of the alpha-stable Ornstein–Uhlenbeck process has the same asymptotic behavior as in tempered stable case. As motivation of our study we calibrate the Ornstein–Uhlenbeck process with tempered stable distribution to real financial data.

Suggested Citation

  • Agnieszka Wylomanska, 2011. "Measures of dependence for Ornstein–Uhlenbeck processes with tempered stable distribution," HSC Research Reports HSC/11/04, Hugo Steinhaus Center, Wroclaw University of Technology.
    • Handle: RePEc:wuu:wpaper:hsc1104
    as

    Download full text from publisher

    File URL: http://www.im.pwr.wroc.pl/~hugo/RePEc/wuu/wpaper/HSC_11_04.pdf
    File Function: Original version, 2011
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Joanna Janczura & Rafal Weron, 2011. "Black swans or dragon kings? A simple test for deviations from the power law," Papers 1102.3712, arXiv.org.
    2. Burnecki, Krzysztof & Misiorek, Adam & Weron, Rafal, 2010. "Loss Distributions," MPRA Paper 22163, University Library of Munich, Germany.
    3. Pavel Cizek & Wolfgang Karl Härdle & Rafal Weron, 2005. "Statistical Tools for Finance and Insurance," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0501, December.
    4. Janczura, Joanna & Weron, Rafal, 2010. "An empirical comparison of alternate regime-switching models for electricity spot prices," Energy Economics, Elsevier, vol. 32(5), pages 1059-1073, September.
    5. Young Kim & Svetlozar Rachev & Michele Bianchi & Frank Fabozzi, 2009. "Computing VAR and AVaR in Infinitely Divisible Distributions," Yale School of Management Working Papers amz2569, Yale School of Management.
    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. Michele Leonardo Bianchi & Svetlozar T. Rachev & Frank J. Fabozzi, 2013. "Tempered stable Ornstein-Uhlenbeck processes: a practical view," Temi di discussione (Economic working papers) 912, Bank of Italy, Economic Research and International Relations Area.
    2. Sikora, Grzegorz & Michalak, Anna & Bielak, Łukasz & Miśta, Paweł & Wyłomańska, Agnieszka, 2019. "Stochastic modeling of currency exchange rates with novel validation techniques," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 523(C), pages 1202-1215.
    3. Szarek, Dawid & Bielak, Łukasz & Wyłomańska, Agnieszka, 2020. "Long-term prediction of the metals’ prices using non-Gaussian time-inhomogeneous stochastic process," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 555(C).

    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. Janczura, Joanna & Weron, Rafal, 2010. "Goodness-of-fit testing for regime-switching models," MPRA Paper 22871, University Library of Munich, Germany.
    2. Bernardi, Mauro & Maruotti, Antonello & Petrella, Lea, 2012. "Skew mixture models for loss distributions: A Bayesian approach," Insurance: Mathematics and Economics, Elsevier, vol. 51(3), pages 617-623.
    3. Burnecki, Krzysztof & Janczura, Joanna & Weron, Rafal, 2010. "Building Loss Models," MPRA Paper 25492, University Library of Munich, Germany.
    4. Joanna Janczura & Sebastian Orzel & Agnieszka Wylomanska, 2011. "Subordinated alpha-stable Ornstein-Uhlenbeck process as a tool for financial data description," HSC Research Reports HSC/11/03, Hugo Steinhaus Center, Wroclaw University of Technology.
    5. Weron, Rafał, 2014. "Electricity price forecasting: A review of the state-of-the-art with a look into the future," International Journal of Forecasting, Elsevier, vol. 30(4), pages 1030-1081.
    6. Joanna Janczura & Rafal Weron, 2012. "Inference for Markov-regime switching models of electricity spot prices," HSC Research Reports HSC/12/01, Hugo Steinhaus Center, Wroclaw University of Technology.
    7. Chernobai, Anna & Burnecki, Krzysztof & Rachev, Svetlozar & Trueck, Stefan & Weron, Rafal, 2005. "Modelling catastrophe claims with left-truncated severity distributions (extended version)," MPRA Paper 10423, University Library of Munich, Germany.
    8. Weron, Rafał & Burnecki, Krzysztof, 2004. "Modeling the risk process in the XploRe computing environment," Papers 2004,08, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    9. Ma, Zong-Gang & Ma, Chao-Qun, 2013. "Pricing catastrophe risk bonds: A mixed approximation method," Insurance: Mathematics and Economics, Elsevier, vol. 52(2), pages 243-254.
    10. Anna Chernobai & Krzysztof Burnecki & Svetlozar Rachev & Stefan Trück & Rafał Weron, 2006. "Modelling catastrophe claims with left-truncated severity distributions," Computational Statistics, Springer, vol. 21(3), pages 537-555, December.
    11. Joanna Janczura & Rafał Weron, 2013. "Goodness-of-fit testing for the marginal distribution of regime-switching models with an application to electricity spot prices," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 97(3), pages 239-270, July.
    12. Rafal Weron, 2006. "Modeling and Forecasting Electricity Loads and Prices: A Statistical Approach," HSC Books, Hugo Steinhaus Center, Wroclaw University of Technology, number hsbook0601, December.
    13. Cui, Yiran & del Baño Rollin, Sebastian & Germano, Guido, 2017. "Full and fast calibration of the Heston stochastic volatility model," European Journal of Operational Research, Elsevier, vol. 263(2), pages 625-638.
    14. Härdle, Wolfgang Karl & Burnecki, Krzysztof & Weron, Rafał, 2004. "Simulation of risk processes," Papers 2004,01, Humboldt University of Berlin, Center for Applied Statistics and Economics (CASE).
    15. Rafał Weron, 2009. "Heavy-tails and regime-switching in electricity prices," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 69(3), pages 457-473, July.
    16. Nowotarski, Jakub & Tomczyk, Jakub & Weron, Rafał, 2013. "Robust estimation and forecasting of the long-term seasonal component of electricity spot prices," Energy Economics, Elsevier, vol. 39(C), pages 13-27.
    17. Tasneem, Faria & Waters, George, 2017. "Forecasting MISO Electricity Prices: A Threshold Autoregressive Approach with Load Data," Journal of Regional Analysis and Policy, Mid-Continent Regional Science Association, vol. 48(3), October.
    18. Afanasyev, Dmitriy O. & Fedorova, Elena A., 2019. "On the impact of outlier filtering on the electricity price forecasting accuracy," Applied Energy, Elsevier, vol. 236(C), pages 196-210.
    19. Chi-Keung Woo, Ira Horowitz, Brian Horii, Ren Orans, and Jay Zarnikau, 2012. "Blowing in the Wind: Vanishing Payoffs of a Tolling Agreement for Natural-gas-fired Generation of Electricity in Texas," The Energy Journal, International Association for Energy Economics, vol. 0(Number 1).
    20. Michal Benko & Wolfgang Härdle & Alois Kneip, 2006. "Common Functional Principal Components," SFB 649 Discussion Papers SFB649DP2006-010, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.

    More about this item

    Keywords

    Ornstein-Uhlenbeck process; alpha-stable distribution; subdiffusion; Measure of dependence; Levy correlation cascade; codifference; interest rates;
    All these keywords.

    JEL classification:

    • C46 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Specific Distributions
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • E47 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Forecasting and Simulation: Models and Applications

    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:wuu:wpaper:hsc1104. 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: Rafal Weron (email available below). General contact details of provider: https://edirc.repec.org/data/hspwrpl.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.