Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes with infinite variance
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We discuss joint temporal and contemporaneous aggregation of N independent copies of random-coefficient AR(1) process driven by i.i.d. 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 a different rate. 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 < (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 Pilipauskaitė and Surgailis (2014) from α = 2 to 0 < α < 2.
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