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The Hodrick-Prescott Filter: Functional aspects and statistical estimation.
Linnaeus University, Faculty of Technology, Department of Mathematics.
2015 (English)Doctoral thesis, comprehensive summary (Other academic)
Place, publisher, year, edition, pages
Växjö: Linnaeus University Press, 2015.
Series
Linnaeus University Dissertations, 218/2015
Keyword [en]
Hodrick-Prescott Filter, Functional data, Estimation, Smoothing Operator.
National Category
Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
URN: urn:nbn:se:lnu:diva-42276ISBN: 978-91-87925-57-3 (print)OAI: oai:DiVA.org:lnu-42276DiVA: diva2:805048
Public defence
2015-05-08, D1136, Växjö, 10:15 (English)
Opponent
Supervisors
Available from: 2015-05-06 Created: 2015-04-14 Last updated: 2015-05-06Bibliographically approved
List of papers
1. A consistent estimator of the smoothing operator in the functional Hodrick-Prescott filter
Open this publication in new window or tab >>A consistent estimator of the smoothing operator in the functional Hodrick-Prescott filter
2017 (English)In: Communications in Statistics - Theory and Methods, ISSN 0361-0926, E-ISSN 1532-415XArticle in journal (Refereed) Epub ahead of print
Abstract [en]

In this paper we consider a version of the functional Hodrick-Prescott ?filter for functional time series. We show that the associated optimal smoothing operator preserves the 'noise-to-signal' structure. Moreover, we propose a consistent estimator of this optimal smoothing operator.

Keyword
consistent estimator, functional Hodrick-Prescott filter, optimal smoothing operator, functional time series
National Category
Other Mathematics
Research subject
Mathematics, Applied Mathematics
Identifiers
urn:nbn:se:lnu:diva-42275 (URN)10.1080/03610926.2017.1346806 (DOI)
Available from: 2015-04-14 Created: 2015-04-14 Last updated: 2017-10-19
2. Functional Hodrick-Prescott Filter
Open this publication in new window or tab >>Functional Hodrick-Prescott Filter
2017 (English)In: Journal of Inverse and Ill-Posed Problems, ISSN 0928-0219, E-ISSN 1569-3945, Vol. 25, no 2, 135-148 p.Article in journal (Refereed) Published
Abstract [en]

We propose a functional version of the Hodrick–Prescott filter for functional data which take values in an infinite-dimensional separable Hilbert space. We further characterize the associated optimal smoothing operator when the associated linear operator is compact and the underlying distribution of the data is Gaussian.

Place, publisher, year, edition, pages
New York: Academic Press, 2017
National Category
Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-24247 (URN)10.1515/jiip-2015-0111 (DOI)000398963900001 ()
Available from: 2013-02-12 Created: 2013-02-12 Last updated: 2017-05-23Bibliographically approved
3. On the Functional Hodrick-Prescott Filter with Non-compact Operators
Open this publication in new window or tab >>On the Functional Hodrick-Prescott Filter with Non-compact Operators
2016 (English)In: Random Operators and Stochastic Equations, ISSN 0926-6364, E-ISSN 1569-397X, Vol. 24, no 1, 33-42 p.Article in journal (Refereed) Published
Abstract [en]

We study a version of the functional Hodrick-Prescott filter where the associated operator is not necessarily compact, but merely closed and densely defined with closed range. We show that the associate doptimal smoothing operator preserves the structure obtained in the compact case, when the underlying distribution of the data is Gaussian.

Keyword
Inverse problems, adaptive estimation, Hodrick–Prescott filter, smoothing, trend extraction, Gaussian measures on a Hilbert space
National Category
Other Mathematics
Research subject
Natural Science, Mathematics
Identifiers
urn:nbn:se:lnu:diva-40160 (URN)10.1515/rose-2016-0003 (DOI)000410277200003 ()2-s2.0-84960539968 (Scopus ID)
Available from: 2015-02-15 Created: 2015-02-15 Last updated: 2017-11-28Bibliographically approved

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Thesis Introduction(243 kB)148 downloads
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