Moment bounds and central limit theorems for Gaussian subordinated arrays

Jean-Marc Bardet and Donatas Surgailis

Journal of Multivariate Analysis, 2013, vol. 114, issue C, 457-473

Abstract: A general moment bound for sums of products of Gaussian vector’s functions extending the moment bound in Taqqu (1977, Lemma 4.5) [28] is established. A general central limit theorem for triangular arrays of nonlinear functionals of multidimensional non-stationary Gaussian sequences is proved. This theorem extends the previous results of Breuer and Major (1983) [5], Arcones (1994) [1] and others. A Berry–Esseen-type bound in the above-mentioned central limit theorem is derived following Nourdin et al. (2011) [20]. Two applications of the above results are discussed. The first one refers to the asymptotic behavior of a roughness statistic for continuous-time Gaussian processes and the second one is a central limit theorem satisfied by long memory locally stationary processes.

Keywords: Central limit theorem for triangular arrays; Moment bound for Gaussian vector’s functions; Hermitian decomposition; Diagram formula; Berry–Esseen bounds; Long memory processes; Locally stationary process (search for similar items in EconPapers)
Date: 2013
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Citations: View citations in EconPapers (6)

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DOI: 10.1016/j.jmva.2012.08.002

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