Testing for long memory in panel random-coefficient AR(1) data
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It is well-known that random-coefficient AR(1) process can have long memory depending on the index β of the tail distribution function of the random coefficient, if it is a regularly varying function at unity. We discuss estimation of β from panel data comprising N random-coefficient AR(1) series, each of length T. The estimator of β 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.
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