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Sample covariances of random-coefficient AR(1) panel model. (English) Zbl 1440.62336
Summary: The present paper obtains a complete description of the limit distributions of sample covariances in $$N\times n$$ panel data when $$N$$ and $$n$$ jointly increase, possibly at different rate. The panel is formed by $$N$$ independent samples of length $$n$$ from random-coefficient AR(1) process with the tail distribution function of the random coefficient regularly varying at the unit root with exponent $$\beta >0$$. We show that for $$\beta\in (0,2)$$ the sample covariances may display a variety of stable and non-stable limit behaviors with stability parameter depending on $$\beta$$ and the mutual increase rate of $$N$$ and $$n$$.

##### MSC:
 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 62D20 Causal inference from observational studies 60F05 Central limit and other weak theorems 62H30 Classification and discrimination; cluster analysis (statistical aspects) 62E20 Asymptotic distribution theory in statistics
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