IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v115y2005i3p417-434.html
   My bibliography  Save this article

Extremes of a class of deterministic sub-sampled processes with applications to stochastic difference equations

Author

Listed:
  • Scotto, M.

Abstract

Let Xk k[greater-or-equal, slanted]1 be a stationary sequence of the formwhere Ak,Bk are i.i.d. -valued random pairs with some given joint distribution. For a strictly increasing subsequence g(k) , let Yk=Xg(k) be the deterministic sub-sampled sequence. The aim of this paper is to look at the limiting form of certain empirical point processes induced by Yk for a specific class of deterministic sampling functions g(·). Such asymptotic results will be useful in obtaining the weak limiting behavior of various functionals of the underlying process including the asymptotic distribution of upper and lower order statistics. In particular, we investigate the limiting distribution of the maximum and its corresponding extremal index.

Suggested Citation

  • Scotto, M., 2005. "Extremes of a class of deterministic sub-sampled processes with applications to stochastic difference equations," Stochastic Processes and their Applications, Elsevier, vol. 115(3), pages 417-434, March.
    • Handle: RePEc:eee:spapps:v:115:y:2005:i:3:p:417-434
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304-4149(04)00154-1
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    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. Dacorogna, Michael M. & Muller, Ulrich A. & Nagler, Robert J. & Olsen, Richard B. & Pictet, Olivier V., 1993. "A geographical model for the daily and weekly seasonal volatility in the foreign exchange market," Journal of International Money and Finance, Elsevier, vol. 12(4), pages 413-438, August.
    2. M. G. Scotto & K. F. Turkman & C. W. Anderson, 2003. "Extremes of Some Sub‐Sampled Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 24(5), pages 579-590, September.
    3. Muller, Ulrich A. & Dacorogna, Michel M. & Olsen, Richard B. & Pictet, Olivier V. & Schwarz, Matthias & Morgenegg, Claude, 1990. "Statistical study of foreign exchange rates, empirical evidence of a price change scaling law, and intraday analysis," Journal of Banking & Finance, Elsevier, vol. 14(6), pages 1189-1208, December.
    4. M. E. Robinson & J. A. Tawn, 2000. "Extremal analysis of processes sampled at different frequencies," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 62(1), pages 117-135.
    5. Hall, A. & Scotto, M. G., 2003. "Extremes of sub-sampled integer-valued moving average models with heavy-tailed innovations," Statistics & Probability Letters, Elsevier, vol. 63(1), pages 97-105, May.
    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. Mladenovic, Pavle, 2009. "Maximum of a partial sample in the uniform AR(1) processes," Statistics & Probability Letters, Elsevier, vol. 79(11), pages 1414-1420, June.

    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. Darmoul Mokhtar & Nizar Harrathi, 2007. "Monetary information arrivals and intraday exchange rate volatility: a comparison of the GARCH and the EGARCH models," Post-Print halshs-00174996, HAL.
    2. Ballocchi, Giuseppe & Dacorogna, Michel M. & Hopman, Carl M. & Muller, Ulrich A. & Olsen, Richard B., 1999. "The intraday multivariate structure of the Eurofutures markets," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 479-513, December.
    3. Seemann, Lars & Hua, Jia-Chen & McCauley, Joseph L. & Gunaratne, Gemunu H., 2012. "Ensemble vs. time averages in financial time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(23), pages 6024-6032.
    4. Bollerslev, Tim & Kretschmer, Uta & Pigorsch, Christian & Tauchen, George, 2009. "A discrete-time model for daily S & P500 returns and realized variations: Jumps and leverage effects," Journal of Econometrics, Elsevier, vol. 150(2), pages 151-166, June.
    5. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    6. Poskitt, Russell, 2008. "Interest rate futures and forwards: Evidence from the sterling futures and FRA markets," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(5), pages 399-412, December.
    7. DeGennaro, Ramon P. & Shrieves, Ronald E., 1997. "Public information releases, private information arrival and volatility in the foreign exchange market," Journal of Empirical Finance, Elsevier, vol. 4(4), pages 295-315, December.
    8. Hua, Jia-Chen & Chen, Lijian & Falcon, Liberty & McCauley, Joseph L. & Gunaratne, Gemunu H., 2015. "Variable diffusion in stock market fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 221-233.
    9. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
    10. Bent Jesper Christensen & Morten Ø. Nielsen, 2005. "The Implied-realized Volatility Relation With Jumps In Underlying Asset Prices," Working Paper 1186, Economics Department, Queen's University.
    11. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    12. Ranaldo, Angelo, 2009. "Segmentation and time-of-day patterns in foreign exchange markets," Journal of Banking & Finance, Elsevier, vol. 33(12), pages 2199-2206, December.
    13. 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.
    14. Kang, Sang Hoon & Yoon, Seong-Min, 2008. "Long memory features in the high frequency data of the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5189-5196.
    15. Bent Jesper Christensen & Morten Ø. Nielsen & Thomas Busch, 2005. "Forecasting Exchange Rate Volatility In The Presence Of Jumps," Working Paper 1187, Economics Department, Queen's University.
    16. Tapiero, Charles S. & Vallois, Pierre, 2016. "Fractional randomness," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 1161-1177.
    17. Nekhili, Ramzi & Altay-Salih, Aslihan & Gençay, Ramazan, 2002. "Exploring exchange rate returns at different time horizons," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 313(3), pages 671-682.
    18. 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.
    19. Bent Jesper Christensen & Morten Ørregaard Nielsen, 2007. "The Effect of Long Memory in Volatility on Stock Market Fluctuations," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 684-700, November.
    20. El-Mekkaoui, Mazen & Flood, Mark D., 1998. "Put-call parity revisited: intradaily tests in the foreign currency options market," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 8(3-4), pages 357-376, December.

    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:spapps:v:115:y:2005:i:3:p:417-434. 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/wps/find/journaldescription.cws_home/505572/description#description .

    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.