IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v153y2017icp121-135.html
   My bibliography  Save this article

Nonparametric estimation of the distribution of the autoregressive coefficient from panel random-coefficient AR(1) data

Author

Listed:
  • Leipus, Remigijus
  • Philippe, Anne
  • Pilipauskaitė, Vytautė
  • Surgailis, Donatas

Abstract

We discuss nonparametric estimation of the distribution function G(x) of the autoregressive coefficient a∈(−1,1) from a panel of N random-coefficient AR(1) data, each of length n, by the empirical distribution function of lag 1 sample autocorrelations of individual AR(1) processes. Consistency and asymptotic normality of the empirical distribution function and a class of kernel density estimators is established under some regularity conditions on G(x) as N and n increase to infinity. The Kolmogorov–Smirnov goodness-of-fit test for simple and composite hypotheses of Beta distributed a is discussed. A simulation study for goodness-of-fit testing compares the finite-sample performance of our nonparametric estimator to the performance of its parametric analogue discussed in Beran et al. (2010).

Suggested Citation

  • Leipus, Remigijus & Philippe, Anne & Pilipauskaitė, Vytautė & Surgailis, Donatas, 2017. "Nonparametric estimation of the distribution of the autoregressive coefficient from panel random-coefficient AR(1) data," Journal of Multivariate Analysis, Elsevier, vol. 153(C), pages 121-135.
    • Handle: RePEc:eee:jmvana:v:153:y:2017:i:c:p:121-135
    DOI: 10.1016/j.jmva.2016.09.007
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X16300902
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2016.09.007?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. Terence Tai-Leung Chong, 2006. "The polynomial aggregated AR(1) model," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 98-122, March.
    2. Granger, C. W. J., 1980. "Long memory relationships and the aggregation of dynamic models," Journal of Econometrics, Elsevier, vol. 14(2), pages 227-238, October.
    3. Dmitrij Celov & Remigijus Leipus & Anne Philippe, 2010. "Asymptotic normality of the mixture density estimator in a disaggregation scheme," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 425-442.
    4. Lajos Horváth & Remigijus Leipus, 2009. "Effect of aggregation on estimators in AR(1) sequence," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 18(3), pages 546-567, November.
    5. Winfried Stute & Wenceslao Manteiga & Manuel Quindimil, 1993. "Bootstrap based goodness-of-fit-tests," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 40(1), pages 243-256, December.
    6. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504, January.
    7. Beran, Jan & Schützner, Martin & Ghosh, Sucharita, 2010. "From short to long memory: Aggregation and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2432-2442, November.
    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. Remigijus Leipus & Anne Philippe & Vytautė Pilipauskaitė & Donatas Surgailis, 2020. "Estimating Long Memory in Panel Random‐Coefficient AR(1) Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 520-535, July.

    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. Anne Philippe & Donata Puplinskaite & Donatas Surgailis, 2014. "Contemporaneous Aggregation Of Triangular Array Of Random-Coefficient Ar(1) Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 35(1), pages 16-39, January.
    2. Jan Beran & Haiyan Liu & Sucharita Ghosh, 2020. "On aggregation of strongly dependent time series," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 47(3), pages 690-710, September.
    3. Remigijus Leipus & Anne Philippe & Vytautė Pilipauskaitė & Donatas Surgailis, 2020. "Estimating Long Memory in Panel Random‐Coefficient AR(1) Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 41(4), pages 520-535, July.
    4. repec:ebl:ecbull:v:3:y:2007:i:2:p:1-10 is not listed on IDEAS
    5. J. Eduardo Vera-Vald'es, 2018. "Nonfractional Memory: Filtering, Antipersistence, and Forecasting," Papers 1801.06677, arXiv.org.
    6. Dmitrij Celov & Remigijus Leipus & Anne Philippe, 2010. "Asymptotic normality of the mixture density estimator in a disaggregation scheme," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 22(4), pages 425-442.
    7. Terence Tai-Leung Chong & Guoxin Liu & Isabel Kit-Ming Yan, 2007. "Habit Formation: Deep and Uncertain," Economics Bulletin, AccessEcon, vol. 3(2), pages 1-10.
    8. Diniz, Ana & Barreiros, João & Crato, Nuno, 2012. "A new model for explaining long-range correlations in human time interval production," Computational Statistics & Data Analysis, Elsevier, vol. 56(6), pages 1908-1919.
    9. Beran, Jan & Schützner, Martin & Ghosh, Sucharita, 2010. "From short to long memory: Aggregation and estimation," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2432-2442, November.
    10. Bernard Candelpergher & Michel Miniconi & Florian Pelgrin, 2015. "Long-memory process and aggregation of AR(1) stochastic processes: A new characterization," Working Papers hal-01166527, HAL.
    11. Baillie, Richard T & Bollerslev, Tim, 1994. "Cointegration, Fractional Cointegration, and Exchange Rate Dynamics," Journal of Finance, American Finance Association, vol. 49(2), pages 737-745, June.
    12. John Barkoulas & Christopher Baum & Mustafa Caglayan, 1999. "Fractional monetary dynamics," Applied Economics, Taylor & Francis Journals, vol. 31(11), pages 1393-1400.
    13. Koop, Gary & Ley, Eduardo & Osiewalski, Jacek & Steel, Mark F. J., 1997. "Bayesian analysis of long memory and persistence using ARFIMA models," Journal of Econometrics, Elsevier, vol. 76(1-2), pages 149-169.
    14. Luis Gil-Alana, 2004. "Forecasting the real output using fractionally integrated techniques," Applied Economics, Taylor & Francis Journals, vol. 36(14), pages 1583-1589.
    15. Anders Johansson, 2009. "An analysis of dynamic risk in the Greater China equity markets," Journal of Chinese Economic and Business Studies, Taylor & Francis Journals, vol. 7(3), pages 299-320.
    16. Jan Babecký & Fabrizio Coricelli & Roman Horváth, 2009. "Assessing Inflation Persistence: Micro Evidence on an Inflation Targeting Economy," Czech Journal of Economics and Finance (Finance a uver), Charles University Prague, Faculty of Social Sciences, vol. 59(2), pages 102-127, June.
    17. SILVESTRINI, Andrea & VEREDAS, David, 2005. "Temporal aggregation of univariate linear time series models," LIDAM Discussion Papers CORE 2005059, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    18. Laurent Davezies & Xavier D'Haultfoeuille & Yannick Guyonvarch, 2019. "Empirical Process Results for Exchangeable Arrays," Papers 1906.11293, arXiv.org, revised May 2020.
    19. Guglielmo Maria Caporale & Luis A. Gil-Alana, 2015. "Infant mortality rates: time trends and fractional integration," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(3), pages 589-602, March.
    20. Michelacci, Claudio & Zaffaroni, Paolo, 2000. "(Fractional) beta convergence," Journal of Monetary Economics, Elsevier, vol. 45(1), pages 129-153, February.
    21. Alexander Frankel & Maximilian Kasy, 2022. "Which Findings Should Be Published?," American Economic Journal: Microeconomics, American Economic Association, vol. 14(1), pages 1-38, 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:jmvana:v:153:y:2017:i:c:p:121-135. 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/622892/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.