an:07221658
Zbl 1446.62248
Pilipauskait??, Vytaut??; Skorniakov, Viktor; Surgailis, Donatas
Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes with infinite variance
EN
Adv. Appl. Probab. 52, No. 1, 237-265 (2020).
00450954
2020
j
62M10 60F05
autoregressive model; panel data; mixture distribution; infinite variance; long-range dependence; scaling transition; Poisson random measure; asymptotic self-similarity
Summary: We discuss the joint temporal and contemporaneous aggregation of \(N\) independent copies of random-coefficient AR(1) processes driven by independent and identically distributed innovations in the domain of normal attraction of an \(\alpha\)-stable distribution, \(0<\alpha\leq 2\), as both \(N\) and the time scale \(n\) tend to infinity, possibly at different rates. Assuming that the tail distribution function of the random autoregressive coefficient regularly varies at the unit root with exponent \(\beta>0\), we show that, for \(\beta<\max(\alpha,1)\), the joint aggregate displays a variety of stable and non-stable limit behaviors with stability index depending on \(\alpha\) , \(\beta\) and the mutual increase rate of \(N\) and \(n\). The paper extends the results of [the first and third authors, Stochastic Processes Appl. 124, No. 2, 1011--1035 (2014; Zbl 1400.62194)] from \(\alpha=2\) to \(0<\alpha<2\).
Zbl 1400.62194