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Estimating long memory in panel random-coefficient AR(1) data

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  • Remigijus Leipus, Vilnius University
  • ,
  • Anne Philippe, Universite de Nantes
  • ,
  • Vytaute Pilipauskaite
  • ,
  • Donatas Surgailis, Vilnius University

We construct an asymptotically normal estimator (Formula presented.) 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 (Formula presented.) 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 (Formula presented.) 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 (Formula presented.), 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.

Original languageEnglish
JournalJournal of Time Series Analysis
Pages (from-to)520-535
Number of pages16
Publication statusPublished - Jul 2020

    Research areas

  • Random-coefficient autoregression, long memory process, measurement error, panel data, tail index estimator

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