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Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes with infinite variance

Part of: Inference from stochastic processes Limit theorems

Published online by Cambridge University Press:  29 April 2020

Vytautė Pilipauskaitė ,
Viktor Skorniakov  and
Donatas Surgailis
Vytautė Pilipauskaitė*
Affiliation:
Aarhus University
Viktor Skorniakov*
Affiliation:
Vilnius University
Donatas Surgailis*
Affiliation:
Vilnius University
*
*Postal address: Aarhus University, Department of Mathematics, Ny Munkegade 118, 8000Aarhus C, Denmark. Email address: [email protected]
*Postal address: Aarhus University, Department of Mathematics, Ny Munkegade 118, 8000Aarhus C, Denmark. Email address: [email protected]
*Postal address: Aarhus University, Department of Mathematics, Ny Munkegade 118, 8000Aarhus C, Denmark. Email address: [email protected]
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Abstract

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, $0< \alpha \le 2$ , 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 Pilipauskaitė and Surgailis (2014) from $\alpha =2$ to $0 < \alpha < 2$ .

Keywords

Autoregressive modelpanel datamixture distributioninfinite variancelong-range dependencescaling transitionPoisson random measureasymptotic self-similarity

MSC classification

Primary: 60F05: Central limit and other weak theorems
Secondary: 62M10: Time series, auto-correlation, regression, etc.
Type
Original Article
Information
Advances in Applied Probability , Volume 52 , Issue 1 , March 2020 , pp. 237 - 265
Copyright
© Applied Probability Trust 2020

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