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.
Publié le : 2017-10-24
Classification:
tail index estimator,
long memory process,
random-coefficient autoregression,
panel data,
MSC 62G32, 62M10.,
[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]
@article{hal-01622201,
author = {Pilipauskaite, Vytaute and Leipus, Remigijus and Philippe, Anne and Surgailis, Donatas},
title = {Testing for long memory in panel random-coefficient AR(1) data},
journal = {HAL},
volume = {2017},
number = {0},
year = {2017},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01622201}
}
Pilipauskaite, Vytaute; Leipus, Remigijus; Philippe, Anne; Surgailis, Donatas. Testing for long memory in panel random-coefficient AR(1) data. HAL, Tome 2017 (2017) no. 0, . http://gdmltest.u-ga.fr/item/hal-01622201/