Linear Processes in Function Spaces

“…In Flores et al (2015) selected two-sample homogenity tests basing on maximal depth elements comparison were discussed. Functional time series are usually defined in terms of functional stochastic processes with values in Banach or Hilbert spaces (Bosq, 2000;Horváth and Kokoszka, 2012). In (Bosq, 2000) it is explained that, probability distribution F of functional random variable does exist.…”

Section: A Concept Of Homogenous Functional Datamentioning

confidence: 99%

“…Functional time series are usually defined in terms of functional stochastic processes with values in Banach or Hilbert spaces (Bosq, 2000;Horváth and Kokoszka, 2012). In (Bosq, 2000) it is explained that, probability distribution F of functional random variable does exist. We look at the random curve X = {X(t), t ∈ [0, T ]} as a random element of the space L 2 = L 2 ([0, T ]) equipped with the Borel σ−algebra.…”

Section: A Concept Of Homogenous Functional Datamentioning

confidence: 99%

Detecting a structural change in functional time series using local Wilcoxon statistic

2017

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Functional data analysis (FDA) (Ramsay et al. (2009);Ramsay and Silverman (2005)) is a part of modern multivariate statistics that analyses data providing information about curves, surfaces or anything else varying over a certain continuum. In economics and empirical finance we often have to deal with time series of functional data, where we cannot easily decide, whether they are to be considered as homogeneous or heterogeneous. At present a discussion on adequate tests of homogenity for functional data is carried (see e.g. Flores et al. (2015)). We propose a novel statistic for detetecting a structural change in functional time series based on a local Wilcoxon statistic induced by a local depth function proposed in Paindaveine and Van Bever (2013).

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“…where (ε i (t), t ∈ [0, 1]; 0 < i ≤ N ) is an H white noise, and operator ρ : H → H is linear and compact [Bosq (2000)]. …”

Section: X(t)y(t)dtmentioning

confidence: 99%

Estimation of the autoregressive operator by wavelet packets

Laukaitis¹,

Vasilecas²,

Laukaitis³

2009

Statistics & Probability Letters

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In this paper, we suggest to use wavelet packet bases as an alternative to the widely used principal component analysis in an estimation of the functional autoregressive processes. By extending the notion of the socalled nonstandard form of operators representation, we search for the "best" basis on a criterion of highest correlation between pairs of wavelet packet coefficients.KEY WORDS:autoregressive Hilbertian process, functional data analysis, wavelet packet bases,ill-posed inverse problem.

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Linear Processes in Function Spaces

Cited by 841 publications

References 0 publications

Adaptive algorithm for stochastic Galerkin method

Adaptive algorithm for stochastic Galerkin method

Detecting a structural change in functional time series using local Wilcoxon statistic

Estimation of the autoregressive operator by wavelet packets

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