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

Vytautė Pilipauskaitė and Donatas Surgailis

Stochastic Processes and their Applications, 2014, vol. 124, issue 2, 1011-1035

Abstract: We discuss joint temporal and contemporaneous aggregation of N independent copies of AR(1) process with random-coefficient a∈[0,1) when N and time scale n increase at different rate. Assuming that a has a density, regularly varying at a=1 with exponent −1<β<1, different joint limits of normalized aggregated partial sums are shown to exist when N1/(1+β)/n tends to (i) ∞, (ii) 0, (iii) 0<μ<∞. The limit process arising under (iii) admits a Poisson integral representation on (0,∞)×C(R) and enjoys ‘intermediate’ properties between fractional Brownian motion limit in (i) and sub-Gaussian limit in (ii).

Keywords: Aggregation; Random-coefficient AR(1) process; Long memory; Intermediate scaling; Asymptotic self-similarity; Poisson stochastic integral (search for similar items in EconPapers)
Date: 2014
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Citations: View citations in EconPapers (9)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:124:y:2014:i:2:p:1011-1035

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DOI: 10.1016/j.spa.2013.10.004

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