Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes |
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Authors: | Vytautė Pilipauskaitė Donatas Surgailis |
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Affiliation: | Vilnius University, Institute of Mathematics and Informatics, Akademijos 4, 08663 Vilnius, Lithuania |
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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). |
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Keywords: | primary, 62M10, 60G22 secondary, 60G15, 60G18, 60G52, 60H05 |
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