IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v101y2015icp73-82.html
   My bibliography  Save this article

Joint aggregation of random-coefficient AR(1) processes with common innovations

Author

Listed:
  • Pilipauskaitė, Vytautė
  • Surgailis, Donatas

Abstract

We discuss joint temporal and contemporaneous aggregation of N copies of stationary random-coefficient AR(1) processes with common i.i.d. standardized innovations, when N and time scale n increase at different rate. Assuming that the random coefficient a has a density, regularly varying at a=1 with exponent −1/2<β<0, different joint limits of normalized aggregated partial sums are shown to exist when N1/(1+β)/n tends to (i) ∞, (ii) 0, (iii) 0<μ<∞. The paper extends the results in Pilipauskaitė and Surgailis (2014) from the case of idiosyncratic innovations to the case of common innovations.

Suggested Citation

  • Pilipauskaitė, Vytautė & Surgailis, Donatas, 2015. "Joint aggregation of random-coefficient AR(1) processes with common innovations," Statistics & Probability Letters, Elsevier, vol. 101(C), pages 73-82.
    • Handle: RePEc:eee:stapro:v:101:y:2015:i:c:p:73-82
    DOI: 10.1016/j.spl.2015.03.002
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715215000826
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2015.03.002?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. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    2. Georges Oppenheim & Marie‐Claude Viano, 2004. "Aggregation of random parameters Ornstein‐Uhlenbeck or AR processes: some convergence results," Journal of Time Series Analysis, Wiley Blackwell, vol. 25(3), pages 335-350, May.
    3. Cremers, Heinz & Kadelka, Dieter, 1986. "On weak convergence of integral functionals of stochastic processes with applications to processes taking paths in LEP," Stochastic Processes and their Applications, Elsevier, vol. 21(2), pages 305-317, February.
    4. 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.
    5. Giraitis, Liudas & Leipus, Remigijus & Surgailis, Donatas, 2010. "Aggregation Of The Random Coefficient Glarch(1,1) Process," Econometric Theory, Cambridge University Press, vol. 26(2), pages 406-425, April.
    6. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.
    7. Gaigalas, Raimundas, 2006. "A Poisson bridge between fractional Brownian motion and stable Lévy motion," Stochastic Processes and their Applications, Elsevier, vol. 116(3), pages 447-462, March.
    8. Zaffaroni, Paolo, 2007. "Aggregation and memory of models of changing volatility," Journal of Econometrics, Elsevier, vol. 136(1), pages 237-249, January.
    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.
    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. Surgailis, Donatas, 2020. "Scaling transition and edge effects for negatively dependent linear random fields on Z2," Stochastic Processes and their Applications, Elsevier, vol. 130(12), pages 7518-7546.
    4. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2017. "Scaling transition for nonlinear random fields with long-range dependence," Stochastic Processes and their Applications, Elsevier, vol. 127(8), pages 2751-2779.

    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. Pilipauskaitė, Vytautė & Surgailis, Donatas, 2014. "Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes," Stochastic Processes and their Applications, Elsevier, vol. 124(2), pages 1011-1035.
    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. 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.
    4. J. Eduardo Vera‐Valdés, 2020. "On long memory origins and forecast horizons," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 39(5), pages 811-826, August.
    5. J. Eduardo Vera-Vald'es, 2018. "Nonfractional Memory: Filtering, Antipersistence, and Forecasting," Papers 1801.06677, arXiv.org.
    6. Caporale, Guglielmo Maria & Gil-Alana, Luis A. & Poza, Carlos, 2020. "High and low prices and the range in the European stock markets: A long-memory approach," Research in International Business and Finance, Elsevier, vol. 52(C).
    7. 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.
    8. Gil-Alana, Luis A. & Mudida, Robert & Zerbo, Eleazar, 2021. "GDP per capita IN SUB-SAHARAN Africa: A time series approach using long memory," International Review of Economics & Finance, Elsevier, vol. 72(C), pages 175-190.
    9. J. Eduardo Vera-Valdés, 2021. "Temperature Anomalies, Long Memory, and Aggregation," Econometrics, MDPI, vol. 9(1), pages 1-22, March.
    10. Haldrup, Niels & Vera Valdés, J. Eduardo, 2017. "Long memory, fractional integration, and cross-sectional aggregation," Journal of Econometrics, Elsevier, vol. 199(1), pages 1-11.
    11. 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.
    12. Thornton, Michael A., 2014. "The aggregation of dynamic relationships caused by incomplete information," Journal of Econometrics, Elsevier, vol. 178(P2), pages 342-351.
    13. 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.
    14. 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.
    15. Maria Kalli & Jim Griffin, 2015. "Flexible Modeling of Dependence in Volatility Processes," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(1), pages 102-113, January.
    16. Fabrizio Coricelli & Roman Horváth, 2010. "Price setting and market structure: an empirical analysis of micro data in Slovakia," Managerial and Decision Economics, John Wiley & Sons, Ltd., vol. 31(2-3), pages 209-233.
    17. Federico Carlini & Paolo Santucci de Magistris, 2019. "Resuscitating the co-fractional model of Granger (1986)," Discussion Papers 19/01, University of Nottingham, Granger Centre for Time Series Econometrics.
    18. Grassi, Stefano & Santucci de Magistris, Paolo, 2014. "When long memory meets the Kalman filter: A comparative study," Computational Statistics & Data Analysis, Elsevier, vol. 76(C), pages 301-319.
    19. Jean Imbs & Eric Jondeau & Florian Pelgrin, 2006. "Aggregating Phillips curves," 2006 Meeting Papers 640, Society for Economic Dynamics.
    20. Kunal Saha & Vinodh Madhavan & Chandrashekhar G. R. & David McMillan, 2020. "Pitfalls in long memory research," Cogent Economics & Finance, Taylor & Francis Journals, vol. 8(1), pages 1733280-173, January.

    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:stapro:v:101:y:2015:i:c:p:73-82. 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.