JOINT TEMPORAL AND CONTEMPORANEOUS AGGREGATION OF RANDOM-COEFFICIENT AR(1) PROCESSES WITH INFINITE VARIANCE

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 α-stable distribution, 0 < α ≥ 2, as both N and the time scale n tend...

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Bibliographic Details
Published inAdvances in applied probability Vol. 52; no. 1; pp. 237 - 265
Main Authors PILIPAUSKAITĖ, VYTAUTĖ, SKORNIAKOV, VIKTOR, SURGAILIS, DONATAS
Format Journal Article
LanguageEnglish
Published Sheffield Applied Probability Trust 01.03.2020
Cambridge University Press
Subjects
Agglomeration
Autoregressive processes
Coefficients
Distribution functions
Longitudinal studies
Original Articles
Probability
Random variables
Sample variance
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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 α-stable distribution, 0 < α ≥ 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 β > 0, we show that, for β < max (α, 1), the joint aggregate displays a variety of stable and non-stable limit behaviors with stability index depending on α, β and the mutual increase rate of N and n. The paper extends the results of Pilipauskaite and Surgailis (2014) from α = 2 to 0 < α < 2.
ISSN:0001-8678
1475-6064
DOI:10.1017/apr.2019.59