IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v443y2016icp170-178.html
   My bibliography  Save this article

Stochastic differential equations applied to the study of geophysical and financial time series

Author

Listed:
  • Mariani, Maria C.
  • Tweneboah, Osei K.

Abstract

This work is devoted to the study of modeling geophysical and financial time series. We propose a stochastic differential equation arising from the superposition of independent Ornstein–Uhlenbeck processes driven by a Γ(a,b) process. Superposition of independent Γ(a,b) Ornstein–Uhlenbeck processes offers analytic flexibility and provides a class of continuous time processes capable of exhibiting long memory behavior. The stochastic differential equation is applied to geophysics and finance by fitting the superposed Γ(a,b) Ornstein–Uhlenbeck model to typical geophysical and financial time series.

Suggested Citation

  • Mariani, Maria C. & Tweneboah, Osei K., 2016. "Stochastic differential equations applied to the study of geophysical and financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 170-178.
    • Handle: RePEc:eee:phsmap:v:443:y:2016:i:c:p:170-178
    DOI: 10.1016/j.physa.2015.09.080
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S037843711500816X
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2015.09.080?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. Mariani, M.C. & Florescu, I. & SenGupta, I. & Beccar Varela, M.P. & Bezdek, P. & Serpa, L., 2013. "Lévy models and scale invariance properties applied to Geophysics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(4), pages 824-839.
    2. Habtemicael, Semere & SenGupta, Indranil, 2014. "Ornstein–Uhlenbeck processes for geophysical data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 147-156.
    3. Mariani, M.C. & Bezdek, P. & Serpa, L. & Florescu, I., 2011. "Ising type models applied to Geophysics and high frequency market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4396-4402.
    4. Bar-Lev, Shaul K. & Bshouty, Daoud & Letac, Gérard, 1992. "Natural exponential families and self-decomposability," Statistics & Probability Letters, Elsevier, vol. 13(2), pages 147-152, January.
    5. Ole E. Barndorff‐Nielsen & Neil Shephard, 2001. "Non‐Gaussian Ornstein–Uhlenbeck‐based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    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. Maria C. Mariani & Peter K. Asante & Md Al Masum Bhuiyan & Maria P. Beccar-Varela & Sebastian Jaroszewicz & Osei K. Tweneboah, 2020. "Long-Range Correlations and Characterization of Financial and Volcanic Time Series," Mathematics, MDPI, vol. 8(3), pages 1-18, March.
    2. Beccar-Varela, Maria P. & Gonzalez-Huizar, Hector & Mariani, Maria C. & Tweneboah, Osei K., 2016. "Use of wavelets techniques to discriminate between explosions and natural earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 42-51.
    3. Semere Habtemicael & Musie Ghebremichael & Indranil SenGupta, 2019. "Volatility and Variance Swap Using Superposition of the Barndorff-Nielsen and Shephard type Lévy Processes," Sankhya B: The Indian Journal of Statistics, Springer;Indian Statistical Institute, vol. 81(1), pages 75-92, June.
    4. Maria P. Beccar-Varela & Md Al Masum Bhuiyan & Maria C. Mariani & Osei K. Tweneboah, 2019. "Analytic Methods for Solving Higher Order Ordinary Differential Equations," Mathematics, MDPI, vol. 7(9), pages 1-17, September.
    5. Beccar-Varela, Maria P. & Mariani, Maria C. & Tweneboah, Osei K. & Florescu, Ionut, 2017. "Analysis of the Lehman Brothers collapse and the Flash Crash event by applying wavelets methodologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 162-171.
    6. Maria C Mariani & Md Al Masum Bhuiyan & Osei K Tweneboah & Hector Gonzalez-Huizar & Ionut Florescu, 2019. "Volatility Models Applied to Geophysics and High Frequency Financial Market Data," Papers 1901.09145, arXiv.org.
    7. Mariani, Maria C. & Bhuiyan, Md Al Masum & Tweneboah, Osei K. & Gonzalez-Huizar, Hector & Florescu, Ionut, 2018. "Volatility models applied to geophysics and high frequency financial market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 503(C), pages 304-321.

    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. Habtemicael, Semere & SenGupta, Indranil, 2014. "Ornstein–Uhlenbeck processes for geophysical data analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 399(C), pages 147-156.
    2. Beccar-Varela, Maria P. & Mariani, Maria C. & Tweneboah, Osei K. & Florescu, Ionut, 2017. "Analysis of the Lehman Brothers collapse and the Flash Crash event by applying wavelets methodologies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 474(C), pages 162-171.
    3. Kanadpriya Basu & Maria C. Mariani & Laura Serpa & Ritwik Sinha, 2015. "Evaluation of Interpolants in Their Ability to Fit Seismometric Time Series," Mathematics, MDPI, vol. 3(3), pages 1-24, August.
    4. Beccar-Varela, Maria P. & Gonzalez-Huizar, Hector & Mariani, Maria C. & Tweneboah, Osei K., 2016. "Use of wavelets techniques to discriminate between explosions and natural earthquakes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 457(C), pages 42-51.
    5. Mariani, Maria C. & Basu, Kanadpriya, 2015. "Spline interpolation techniques applied to the study of geophysical data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 428(C), pages 68-79.
    6. Madan, Dilip B. & Wang, King, 2021. "The structure of financial returns," Finance Research Letters, Elsevier, vol. 40(C).
    7. Dimitrios D. Thomakos & Michail S. Koubouros, 2011. "The Role of Realised Volatility in the Athens Stock Exchange," Multinational Finance Journal, Multinational Finance Journal, vol. 15(1-2), pages 87-124, March - J.
    8. Taufer, Emanuele & Leonenko, Nikolai, 2009. "Simulation of Lvy-driven Ornstein-Uhlenbeck processes with given marginal distribution," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2427-2437, April.
    9. Torben G. Andersen & Tim Bollerslev & Peter Christoffersen & Francis X. Diebold, 2007. "Practical Volatility and Correlation Modeling for Financial Market Risk Management," NBER Chapters, in: The Risks of Financial Institutions, pages 513-544, National Bureau of Economic Research, Inc.
    10. Lars Stentoft, 2008. "American Option Pricing Using GARCH Models and the Normal Inverse Gaussian Distribution," Journal of Financial Econometrics, Oxford University Press, vol. 6(4), pages 540-582, Fall.
    11. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," The Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
    12. Ole Barndorff-Nielsen & Neil Shephard, 2004. "Multipower Variation and Stochastic Volatility," Economics Papers 2004-W30, Economics Group, Nuffield College, University of Oxford.
    13. Álvaro Cartea & Thilo Meyer-Brandis, 2010. "How Duration Between Trades of Underlying Securities Affects Option Prices," Review of Finance, European Finance Association, vol. 14(4), pages 749-785.
    14. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
    15. Jondeau, Eric, 2016. "Asymmetry in tail dependence in equity portfolios," Computational Statistics & Data Analysis, Elsevier, vol. 100(C), pages 351-368.
    16. A. Aghamohammadi & S. Mohammadi, 2017. "Bayesian analysis of penalized quantile regression for longitudinal data," Statistical Papers, Springer, vol. 58(4), pages 1035-1053, December.
    17. Robert Brooks & Robert Faff & Sirimon Treepongkaruna & Eliza Wu, 2015. "Do Sovereign Re-Ratings Destabilize Equity Markets during Financial Crises? New Evidence from Higher Return Moments," Journal of Business Finance & Accounting, Wiley Blackwell, vol. 42(5-6), pages 777-799, June.
    18. Piotr Szczepocki, 2020. "Application of iterated filtering to stochastic volatility models based on non-Gaussian Ornstein-Uhlenbeck process," Statistics in Transition New Series, Polish Statistical Association, vol. 21(2), pages 173-187, June.
    19. Caravenna, Francesco & Corbetta, Jacopo, 2018. "The asymptotic smile of a multiscaling stochastic volatility model," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 1034-1071.
    20. F. Javier Mencía & Enrique Sentana, 2004. "Estimation and Testing of Dynamic Models with Generalised Hyperbolic Innovations," Working Papers wp2004_0411, CEMFI.

    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:phsmap:v:443:y:2016:i:c:p:170-178. 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.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.