Sample covariances of random-coefficient AR(1) panel model

Remigijus Leipus (1) , Anne Philippe (2) , Vytaute Pilipauskaite (3) , Donatas Surgailis (1)

1 Vilnius Institute of Mathematics and Informatics
2 LMJL - Laboratoire de Mathématiques Jean Leray
3 Aarhus University [Aarhus]

The present paper obtains a complete description of the limit distributions of sample covariances in N × n panel data when N and n jointly increase, possibly at different rate. The panel is formed by N independent samples of length n from random-coefficient AR(1) process with the tail distribution function of the random coefficient regularly varying at the unit root with exponent β > 0. We show that for β ∈ (0, 2) the sample covariances may display a variety of stable and non-stable limit behaviors with stability parameter depending on β and the mutual increase rate of N and n.

Mots clés: Autoregressive model; Panel data; Mixture distribution; Long memory; Sample covariance; Scaling transition; Poisson random measure; Asymptotic self-similarity

Domaines: Statistiques [math.ST]

Remigijus Leipus, Anne Philippe, Vytaute Pilipauskaite, Donatas Surgailis. Sample covariances of random-coefficient AR(1) panel model. 2019. ⟨hal-01903304v2⟩