IDEAS home Printed from https://ideas.repec.org/a/qnt/quantl/y2012i10p1-31.html
   My bibliography  Save this article

Dependence and stochastic limit theory (in Russian)

Author

Listed:
  • Jonathan Hill

    (University of North Carolina, Chapel Hill, USA)

Abstract

In this essay we provide the basic asymptotic theory that serves as background theory for estimators in time series. We outline concepts of dependence used for stochastic limit theory, covering mixing, mixingale and near epoch dependence properties. We then detail some of the most general probability and distribution limit theorems for these processes popularly employed for time series theory and applications.

Suggested Citation

  • Jonathan Hill, 2012. "Dependence and stochastic limit theory (in Russian)," Quantile, Quantile, issue 10, pages 1-31, December.
    • Handle: RePEc:qnt:quantl:y:2012:i:10:p:1-31
    as

    Download full text from publisher

    File URL: http://quantile.ru/10/10-JH.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Davidson, James, 1994. "Stochastic Limit Theory: An Introduction for Econometricians," OUP Catalogue, Oxford University Press, number 9780198774037.
    2. L. Mokliachuk & I. Horodyska & V. Monarkh & O. Mokliachuk & T. Mokliachuk, 2017. "Assessment of environmental risks in toxic chemicals zones," Balanced Nature Using, Institute of agroecology and environmental management, vol. 7(3), pages 145-151, September.
    3. de Jong, Robert M. & Davidson, James, 2000. "The Functional Central Limit Theorem And Weak Convergence To Stochastic Integrals I," Econometric Theory, Cambridge University Press, vol. 16(5), pages 621-642, October.
    4. H.J. Bierens, 1981. "Robust Methods and Asymptotic Theory in Nonlinear Econometrics," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 35(3), pages 173-173, September.
    5. FAUCOMPRET, Erik & MEERSMAN, Hilde & GEERAERT, Emiel & JEGERS, Marc & HENDRICKX, Koen & VAN DE VOORDE, Eddy & NONNEMAN, Walter & ROOSENS, Paul & VANHOUDT, Patrick & KERSTENS, Kristiaan & BLAUWENS, G. , 1996. "FAUCOMPRET, Erik: "Europe's post-war recovery (Barry EICHENGREEN, Cambridge University Press, 1995)" (p. 527); MEERSMAN, Hilde: "Applied econometric time series (Walter ENDERS, John Wil," Economic and Social Journal (Economisch en Sociaal Tijdschrift), University of Antwerp, Faculty of Business and Economics, vol. 50(3), pages 527-551, September.
    6. de Jong, Robert M., 1997. "Central Limit Theorems for Dependent Heterogeneous Random Variables," Econometric Theory, Cambridge University Press, vol. 13(3), pages 353-367, June.
    7. Eckhard Liebscher, 2005. "Towards a Unified Approach for Proving Geometric Ergodicity and Mixing Properties of Nonlinear Autoregressive Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(5), pages 669-689, September.
    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. Calhoun, Gray, 2014. "Block Bootstrap Consistency Under Weak Assumptions," Staff General Research Papers Archive 34313, Iowa State University, Department of Economics.
    2. Qiu, Jin & Ma, Qing & Wu, Lang, 2019. "A moving blocks empirical likelihood method for panel linear fixed effects models with serial correlations and cross-sectional dependences," Economic Modelling, Elsevier, vol. 83(C), pages 394-405.
    3. Kapetanios, G. & Pesaran, M. Hashem & Yamagata, T., 2011. "Panels with non-stationary multifactor error structures," Journal of Econometrics, Elsevier, vol. 160(2), pages 326-348, February.
    4. Yang, Lixiong & Lee, Chingnun & Shie, Fu Shuen, 2014. "How close a relationship does a capital market have with other markets? A reexamination based on the equal variance test," Pacific-Basin Finance Journal, Elsevier, vol. 26(C), pages 198-226.
    5. Qiu, Jin & Lin, Zhengyan, 2006. "The variance of partial sums of strong near-epoch dependent variables," Statistics & Probability Letters, Elsevier, vol. 76(17), pages 1845-1854, November.
    6. de Jong, Robert M. & Woutersen, Tiemen, 2011. "Dynamic Time Series Binary Choice," Econometric Theory, Cambridge University Press, vol. 27(4), pages 673-702, August.
    7. Kapetanios, G. & Mitchell, J. & Price, S. & Fawcett, N., 2015. "Generalised density forecast combinations," Journal of Econometrics, Elsevier, vol. 188(1), pages 150-165.
    8. Burak Alparslan Eroğlu & J. Isaac Miller & Taner Yiğit, 2022. "Time-varying cointegration and the Kalman filter," Econometric Reviews, Taylor & Francis Journals, vol. 41(1), pages 1-21, January.
    9. J. Isaac Miller, 2010. "Cointegrating regressions with messy regressors and an application to mixed‐frequency series," Journal of Time Series Analysis, Wiley Blackwell, vol. 31(4), pages 255-277, July.
    10. Robert F. Engle & Aaron D. Smith, 1999. "Stochastic Permanent Breaks," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 553-574, November.
    11. Blasques, F. & Francq, Christian & Laurent, Sébastien, 2023. "Quasi score-driven models," Journal of Econometrics, Elsevier, vol. 234(1), pages 251-275.
    12. Miller J. Isaac, 2010. "A Nonlinear IV Likelihood-Based Rank Test for Multivariate Time Series and Long Panels," Journal of Time Series Econometrics, De Gruyter, vol. 2(1), pages 1-38, September.
    13. Isao Ishida & Virmantas Kvedaras, 2015. "Modeling Autoregressive Processes with Moving-Quantiles-Implied Nonlinearity," Econometrics, MDPI, vol. 3(1), pages 1-53, January.
    14. Sandberg, Rickard, 2016. "Trends, unit roots, structural changes, and time-varying asymmetries in U.S. macroeconomic data: the Stock and Watson data re-examined," Economic Modelling, Elsevier, vol. 52(PB), pages 699-713.
    15. H. Peter Boswijk & Yang Zu, 2022. "Adaptive Testing for Cointegration With Nonstationary Volatility," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 40(2), pages 744-755, April.
    16. Andreou, Elena & Ghysels, Eric, 2006. "Monitoring disruptions in financial markets," Journal of Econometrics, Elsevier, vol. 135(1-2), pages 77-124.
    17. Andrews, Donald W.K. & Guggenberger, Patrik, 2017. "Asymptotic Size Of Kleibergen’S Lm And Conditional Lr Tests For Moment Condition Models," Econometric Theory, Cambridge University Press, vol. 33(5), pages 1046-1080, October.
    18. George Kapetanios & Zacharias Psaradakis, 2016. "Semiparametric Sieve-Type Generalized Least Squares Inference," Econometric Reviews, Taylor & Francis Journals, vol. 35(6), pages 951-985, June.
    19. Davidson, James, 2002. "Establishing conditions for the functional central limit theorem in nonlinear and semiparametric time series processes," Journal of Econometrics, Elsevier, vol. 106(2), pages 243-269, February.
    20. Mynbayev, Kairat & Darkenbayeva, Gulsim, 2019. "Analyzing variance in central limit theorems," MPRA Paper 101685, University Library of Munich, Germany.

    More about this item

    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:qnt:quantl:y:2012:i:10:p:1-31. 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 Anatolyev (email available below). General contact details of provider: http://quantile.ru/ .

    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.