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Joint temporal and contemporaneous aggregation of random-coefficient AR(1) processes with infinite variance. (English) Zbl 1446.62248
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 $$\alpha$$-stable distribution, $$0<\alpha\leq 2$$, 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 [the first and third authors, Stochastic Processes Appl. 124, No. 2, 1011–1035 (2014; Zbl 1400.62194)] from $$\alpha=2$$ to $$0<\alpha<2$$.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60F05 Central limit and other weak theorems
longmemo
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