The integrated periodogram for long-memory processes with finite or infinite variance
type: Item
instance of: scholarly article
title: The integrated periodogram for long-memory processes with finite or infinite variance
zbMATH Open document ID: 0885.62108
DOI: 10.1016/S0304-4149(96)00124-X
published in: Stochastic Processes and their Applications
publication date: 1998-03-29T00:00:00Z
review text: The authors consider the stationary linear processes in the form \[ X_t=\sum _{j=0}^\infty c_jZ_{t-j}, \qquad t\in \mathcal {Z}, \] with a noise sequence \((Z_t)_{t\in \mathcal {Z}}\) of i.i.d. random variables which may have finite or infinite variance. The model may exhibit long-range dependence. The integrated periodogram \(K_n(\lambda )\) can be interpreted as the relative error of the empirical spectral density compared with the true spectral density in the interval \([0,\lambda ]\). The authors derive functional limit theorems for the randomly centered sequence \[ \left (K_n(\lambda )-K_n(\pi ){{\lambda +\pi }\over {2\pi }} \right )_{\lambda \in [-\pi ,\pi ]} \] The results are applied to obtain corresponding Kolmogorov--Smirnov and Cramér--von Mises goodness-of-fit tests.
Mathematics Subject Classification ID: 62M15
Mathematics Subject Classification ID: 60F17
Mathematics Subject Classification ID: 62M10
Mathematics Subject Classification ID: 62G10
zbMATH DE Number: 1134806
zbMATH Keywords: integrated periodogram
zbMATH Keywords: long-memory
zbMATH Keywords: heavy tails
zbMATH Keywords: functional limit theorems
zbMATH Keywords: goodness-of-fit tests
zbMATH Keywords: fractional ARIMA
author: Piotr Kokoszka
author: T. Mikosch
reviewed by: Gejza Dohnal
describes a project that uses: longmemo
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1134806