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From short to long memory: Aggregation and estimation

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  • Beran, Jan
  • Schützner, Martin
  • Ghosh, Sucharita

Abstract

Contemporaneous aggregation of asymptotically stationary AR(1) processes is considered where the squared random coefficients are beta-distributed. Based on the sample correlation coefficients for the individual AR(1) processes, an estimator for the parameters of the underlying beta distribution, and thus for the long memory parameter of the aggregated process, is introduced. Consistency and asymptotic normality are derived and the new estimator is shown to be asymptotically equivalent to the maximum likelihood estimator of the beta distribution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:csdana:v:54:y:2010:i:11:p:2432-2442
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    References listed on IDEAS

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    1. Kazakevicius, Vytautas & Leipus, Remigijus & Viano, Marie-Claude, 2004. "Stability of random coefficient ARCH models and aggregation schemes," Journal of Econometrics, Elsevier, vol. 120(1), pages 139-158, May.
    2. Paolo Zaffaroni, 2007. "Contemporaneous aggregation of GARCH processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(4), pages 521-544, July.
    3. Terence Tai-Leung Chong, 2006. "The polynomial aggregated AR(1) model," Econometrics Journal, Royal Economic Society, vol. 9(1), pages 98-122, March.
    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. Marco Lippi & Paolo Zaffaroni, 1998. "Aggregation of Simple Linear Dynamics: Exact Asymptotic Results," STICERD - Econometrics Paper Series 350, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    6. Henghsiu Tsai & K. S. Chan, 2005. "Temporal Aggregation of Stationary And Nonstationary Discrete‐Time Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(4), pages 613-624, July.
    7. Zaffaroni, Paolo, 2004. "Contemporaneous aggregation of linear dynamic models in large economies," Journal of Econometrics, Elsevier, vol. 120(1), pages 75-102, May.
    8. Alain Breton & Dinh Pham, 1989. "On the bias of the least squares estimator for the first order autoregressive process," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 41(3), pages 555-563, September.
    9. Beran, Jan & Ocker, Dirk, 2000. "Temporal aggregation of stationary and nonstationary FARIMA (p, d, 0) models," CoFE Discussion Papers 00/22, University of Konstanz, Center of Finance and Econometrics (CoFE).
    10. Zaffaroni, Paolo, 2007. "Aggregation and memory of models of changing volatility," Journal of Econometrics, Elsevier, vol. 136(1), pages 237-249, January.
    11. 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.
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    1. 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.
    2. 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.
    3. J. Eduardo Vera-Vald'es, 2018. "Nonfractional Memory: Filtering, Antipersistence, and Forecasting," Papers 1801.06677, arXiv.org.
    4. 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.
    5. 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.
    6. 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.

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