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Article overview
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Weak convergence of the function-indexed integrated periodogram for infinite variance processes | Sami Umut Can
; Thomas Mikosch
; Gennady Samorodnitsky
; | Date: |
23 Nov 2010 | Abstract: | In this paper, we study the weak convergence of the integrated periodogram
indexed by classes of functions for linear processes with symmetric
$alpha$-stable innovations. Under suitable summability conditions on the
series of the Fourier coefficients of the index functions, we show that the
weak limits constitute $alpha$-stable processes which have representations as
infinite Fourier series with i.i.d. $alpha$-stable coefficients. The cases
$alphain(0,1)$ and $alphain[1,2)$ are dealt with by rather different
methods and under different assumptions on the classes of functions. For
example, in contrast to the case $alphain(0,1)$, entropy conditions are
needed for $alphain[1,2)$ to ensure the tightness of the sequence of
integrated periodograms indexed by functions. The results of this paper are of
additional interest since they provide limit results for infinite mean random
quadratic forms with particular Toeplitz coefficient matrices. | Source: | arXiv, 1011.5062 | Services: | Forum | Review | PDF | Favorites |
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