IDEAS home Printed from https://ideas.repec.org/a/eee/spapps/v128y2018i3p819-846.html
   My bibliography  Save this article

On a notion of partially conditionally identically distributed sequences

Author

Listed:
  • Fortini, Sandra
  • Petrone, Sonia
  • Sporysheva, Polina

Abstract

A notion of conditionally identically distributed (c.i.d.) sequences has been studied as a form of stochastic dependence weaker than exchangeability, but equivalent to it in the presence of stationarity. We extend such notion to families of sequences. Paralleling the extension from exchangeability to partial exchangeability in the sense of de Finetti, we propose a notion of partially c.i.d. dependence, which is shown to be equivalent to partial exchangeability for stationary processes. Partially c.i.d. families of sequences preserve attractive limit properties of partial exchangeability, and are asymptotically partially exchangeable. Moreover, we provide strong laws of large numbers and two central limit theorems. Our focus is on the asymptotic agreement of predictions and empirical means, which lies at the foundations of Bayesian statistics. Natural examples of partially c.i.d. constructions are interacting randomly reinforced processes satisfying certain conditions on the reinforcement.

Suggested Citation

  • Fortini, Sandra & Petrone, Sonia & Sporysheva, Polina, 2018. "On a notion of partially conditionally identically distributed sequences," Stochastic Processes and their Applications, Elsevier, vol. 128(3), pages 819-846.
    • Handle: RePEc:eee:spapps:v:128:y:2018:i:3:p:819-846
    DOI: 10.1016/j.spa.2017.06.008
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0304414917301631
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spa.2017.06.008?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. Nancy Flournoy & Caterina May & Piercesare Secchi, 2012. "Asymptotically Optimal Response-Adaptive Designs for Allocating the Best Treatment: An Overview," International Statistical Review, International Statistical Institute, vol. 80(2), pages 293-305, August.
    2. Edoardo M. Airoldi & Thiago Costa & Federico Bassetti & Fabrizio Leisen & Michele Guindani, 2014. "Generalized Species Sampling Priors With Latent Beta Reinforcements," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 109(508), pages 1466-1480, December.
    3. Beggs, A.W., 2005. "On the convergence of reinforcement learning," Journal of Economic Theory, Elsevier, vol. 122(1), pages 1-36, May.
    4. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    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. Berti, Patrizia & Dreassi, Emanuela & Pratelli, Luca & Rigo, Pietro, 2021. "Asymptotics of certain conditionally identically distributed sequences," Statistics & Probability Letters, Elsevier, vol. 168(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. Michele Guindani & Wesley O. Johnson, 2018. "More nonparametric Bayesian inference in applications," Statistical Methods & Applications, Springer;Società Italiana di Statistica, vol. 27(2), pages 239-251, June.
    2. Dash, Saumya Ranjan & Maitra, Debasish, 2018. "Does sentiment matter for stock returns? Evidence from Indian stock market using wavelet approach," Finance Research Letters, Elsevier, vol. 26(C), pages 32-39.
    3. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    4. Dufour, Jean-Marie & García, René, 2008. "Measuring causality between volatility and returns with high-frequency data," UC3M Working papers. Economics we084422, Universidad Carlos III de Madrid. Departamento de Economía.
    5. Kaijian He & Rui Zha & Jun Wu & Kin Keung Lai, 2016. "Multivariate EMD-Based Modeling and Forecasting of Crude Oil Price," Sustainability, MDPI, vol. 8(4), pages 1-11, April.
    6. Ozcan Ceylan, 2015. "Limited information-processing capacity and asymmetric stock correlations," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1031-1039, June.
    7. Scalas, Enrico & Kaizoji, Taisei & Kirchler, Michael & Huber, Jürgen & Tedeschi, Alessandra, 2006. "Waiting times between orders and trades in double-auction markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 463-471.
    8. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    9. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Oxford University Press, vol. 4(1), pages 1-30.
    10. Monira Essa Aloud, 2016. "Time Series Analysis Indicators under Directional Changes: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 55-64.
    11. Vassilios G. Papavassiliou, 2016. "Allowing For Jump Measurements In Volatility: A High-Frequency Financial Data Analysis Of Individual Stocks," Bulletin of Economic Research, Wiley Blackwell, vol. 68(2), pages 124-132, April.
    12. Monira Essa Aloud, 2016. "Profitability of Directional Change Based Trading Strategies: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 87-95.
    13. Cotter, John & Dowd, Kevin, 2007. "The tail risks of FX return distributions: A comparison of the returns associated with limit orders and market orders," Finance Research Letters, Elsevier, vol. 4(3), pages 146-154, September.
    14. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    15. Stefanescu, Razvan & Dumitriu, Ramona, 2015. "Conţinutul analizei seriilor de timp financiare [The Essentials of the Analysis of Financial Time Series]," MPRA Paper 67175, University Library of Munich, Germany.
    16. Challet, Damien & Stinchcombe, Robin, 2003. "Limit order market analysis and modelling: on a universal cause for over-diffusive prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 141-145.
    17. Feng, Yuanhua, 2002. "Modelling Different Volatility Components," CoFE Discussion Papers 02/18, University of Konstanz, Center of Finance and Econometrics (CoFE).
    18. Caporin, Massimiliano & Chang, Chia-Lin & McAleer, Michael, 2019. "Are the S&P 500 index and crude oil, natural gas and ethanol futures related for intra-day data?," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 50-70.
    19. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.
    20. Julien Chevallier & Benoît Sévi, 2011. "On the realized volatility of the ECX CO 2 emissions 2008 futures contract: distribution, dynamics and forecasting," Annals of Finance, Springer, vol. 7(1), pages 1-29, February.

    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:128:y:2018:i:3:p:819-846. 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.