Title: Testing for long memory in panel random-coefficient AR(1) data,
Abstract: It is well-known that random-coefficient AR(1) process can have long memory
depending on the index $\beta$ of the tail distribution function of the random
coefficient, if it is a regularly varying function at unity. We discuss
estimation of $\beta$ from panel data comprising N random-coefficient AR(1)
series, each of length T. The estimator of $\beta$ is constructed as a version
of the tail index estimator of Goldie and Smith (1987) applied to sample lag 1
autocorrelations of individual time series. Its asymptotic normality is derived
under 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 panel
random-coefficient AR(1) data exhibit long memory. A simulation study
illustrates finite-sample performance of the introduced estimator and testing
procedure.