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

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  • 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
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    References listed on IDEAS

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    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. Vaart,A. W. van der, 2000. "Asymptotic Statistics," Cambridge Books, Cambridge University Press, number 9780521784504.
    4. 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.
    5. 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.
    6. 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.
    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.
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    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.

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