
Spectral representations of weakly stationary processes valued in a separable Hilbert space : a survey with applications on functional time series
In this paper, we review and clarify the construction of a spectral theo...
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A note on Herglotz's theorem for time series on function spaces
In this article, we prove Herglotz's theorem for Hilbertvalued time ser...
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A general white noise test based on kernel lagwindow estimates of the spectral density operator
We propose a general white noise test for functional time series based o...
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Cointegrated DensityValued Linear Processes
In data rich environments we may sometimes deal with time series that ar...
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A Hilbert Space of Stationary Ergodic Processes
Identifying meaningful signal buried in noise is a problem of interest a...
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Kendall's Tau for Functional Data Analysis
We treat the problem of testing for association between a functional var...
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A test for Gaussianity in Hilbert spaces via the empirical characteristic functional
Let X_1,X_2, ... be independent and identically distributed random eleme...
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The maximum of the periodogram of Hilbert space valued time series
We are interested to detect periodic signals in Hilbert space valued time series when the length of the period is unknown. A natural test statistic is the maximum HilbertSchmidt norm of the periodogram operator over all fundamental frequencies. In this paper we analyze the asymptotic distribution of this test statistic. We consider the case where the noise variables are independent and then generalize our results to functional linear processes. Details for implementing the test are provided for the class of functional autoregressive processes. We illustrate the usefulness of our approach by examining air quality data from Graz, Austria. The accuracy of the asymptotic theory in finite samples is evaluated in a simulation experiment.
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