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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 \(0<\alpha<2\).

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