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Joint aggregation of random-coefficient AR(1) processes with common innovations. (English) Zbl 1325.62171
Summary: We discuss joint temporal and contemporaneous aggregation of $$N$$ copies of stationary random-coefficient AR(1) processes with common i.i.d. standardized innovations, when $$N$$ and time scale $$n$$ increase at different rate. Assuming that the random coefficient $$a$$ has a density, regularly varying at $$a = 1$$ with exponent $$- 1 / 2 < \beta < 0$$, different joint limits of normalized aggregated partial sums are shown to exist when $$N^{1 /(1 + \beta)} / n$$ tends to (i) $$\infty$$, (ii) 0, (iii) $$0 < \mu < \infty$$. The paper extends the results in [the authors, Stochastic Processes Appl. 124, No. 2, 1011–1035 (2014; Zbl 1400.62194)] from the case of idiosyncratic innovations to the case of common innovations.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60G22 Fractional processes, including fractional Brownian motion 60G15 Gaussian processes 60G18 Self-similar stochastic processes 60H05 Stochastic integrals
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