Testing for Long Memory in Random-coefficient AR(1) Panel
Donatas Surgailis, Institute of Mathematics and Informatics, Vilnius University, Lithuania
It is well-known since Granger (1980) that random-coefficient AR(1) process can have long memory covariance,
if the tail distribution function of the random coefficient regularly varies at the unit root with exponent
β ∊ (1,2). This talk discusses statistical inference for N x T panel consisting of N independent RCAR(1)
series, each of length T, as N and T jointly increase possibly at a different rate. In the first part, we discuss
the asymptotic distribution of the sample mean and the sample variance for the above panel and show that these
distributions crucially depend on the mutual increase rate of N, T, with the critical rate 
separating different limit regimes. The second part deals with nonparametric estimation of β for the same panel.
The estimator 
is constructed as a version of the tail index estimator of Goldie and
Smith (1987) applied to the serial correlation coefficients of each of N rows. The asymptotic normality of is
obtained under certain conditions on N, T, β and some other quantities of our statistical model. Based on this result, we construct a statistical
test to test the null hypothesis β ≥ 2 against the alternative β<2, or that the RCAR(1) panel data exhibit long memory. A simulation study
illustrates finite-sample performance of the introduced estimator and testing procedure.
This is joint work with Remigijus Leipus, Anne Philippe, and Vytaute Pilipauskaite