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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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