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Title: Testing for long memory in panel random-coefficient AR(1) data Authors:  Remigijus Leipus - Vilnius University (Lithuania)
Anne Philippe - Universite de Nantes (France) [presenting]
Vytaute Pilipauskaite - Vilnius University - Universite de Nantes (Lithuania)
Donatas Surgailis - Vilnius university - Institute of mathematics and informatics (Lithuania)
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 the 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 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.