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It is well-known that random-coefficient AR(1) process can have long memorydepending on the index $\beta$ of the tail distribution function of the randomcoefficient, if it is a regularly varying function at unity. We discussestimation of $\beta$ from panel data comprising N random-coefficient AR(1)series, each of length T. The estimator of $\beta$ is constructed as a versionof the tail index estimator of Goldie and Smith (1987) applied to sample lag 1autocorrelations of individual time series. Its asymptotic normality is derivedunder certain conditions on N, T and some parameters of our statistical model.Based on this result, we construct a statistical procedure to test if the panelrandom-coefficient AR(1) data exhibit long memory. A simulation studyillustrates finite-sample performance of the introduced estimator and testingprocedure.

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