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

Remigijus Leipus, Anne Philippe, Vytautė Pilipauskaitė and Donatas Surgailis

Journal of Time Series Analysis, 2020, vol. 41, issue 4, 520-535

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.

Date: 2020
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