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Estimating Long Memory in Panel Random‐Coefficient AR(1) Data

Author

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  • Remigijus Leipus
  • Anne Philippe
  • Vytautė Pilipauskaitė
  • Donatas Surgailis

Abstract

We construct an asymptotically normal estimator β˜N for the tail index β of a distribution on (0,1) regularly varying at x=1, when its N independent realizations are not directly observable. The estimator β˜N is a version of the tail index estimator of Goldie and Smith (1987) [Goldie CM, Smith RL. 1987. The Quarterly Journal of Mathematics 38: 45–71] based on suitably truncated observations contaminated with arbitrarily dependent ‘noise’ which vanishes as N increases. We apply β˜N to panel data comprising N random‐coefficient AR(1) series, each of length T, for estimation of the tail index of the random coefficient at the unit root, in which case the unobservable random coefficients are replaced by sample lag 1 autocorrelations of individual time series. Using asymptotic normality of β˜N, we construct a statistical procedure to test if the panel random‐coefficient AR(1) data exhibit long memory. A simulation study illustrates finite‐sample performance of the introduced inference procedures.

Suggested Citation

  • 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.
    • Handle: RePEc:bla:jtsera:v:41:y:2020:i:4:p:520-535
    DOI: 10.1111/jtsa.12519
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    References listed on IDEAS

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