Functional Time Series

Siegfried Hörmann, Piotr P. Kokoszka

Research output: Chapter in Book/Report/Conference proceedingChapter

Abstract

This chapter is an account of the recent research that deals with curves observed consecutively over time. The curves are viewed in the framework of functional data analysis, that is, each of them is considered as a whole statistical object. We describe the Hilbert space framework within which the mathematical foundations are developed. We then introduce the most popular model for such data, the functional autoregressive process, and discuss its properties. This is followed by the introduction of a general framework that quantifies the temporal dependence of curves. Within this framework, we discuss analogs of central concepts of time series analysis of scalar data, including the definition and the estimation of an analog of the long-run variance.
LanguageEnglish
Title of host publicationTime Series Analysis
Subtitle of host publicationMethods and Applications
EditorsTata Subba Rao
Place of PublicationAmsterdam
PublisherElsevier B.V.
Pages157-186
Number of pages30
Volume30
ISBN (Print)978-0-444-53858-1
DOIs
StatusPublished - 2012

Publication series

NameHandbook of Statistics
Volume30
ISSN (Print)0169-7161

Fingerprint

Time series
Curve
Analogue
Functional Data Analysis
Autoregressive Process
Time Series Analysis
Long-run
Quantify
Hilbert space
Scalar
Framework
Model

Cite this

Hörmann, S., & Kokoszka, P. P. (2012). Functional Time Series. In T. S. Rao (Ed.), Time Series Analysis: Methods and Applications (Vol. 30, pp. 157-186). (Handbook of Statistics; Vol. 30). Amsterdam: Elsevier B.V.. DOI: 10.1016/B978-0-444-53858-1.00007-7

Functional Time Series. / Hörmann, Siegfried; Kokoszka, Piotr P.

Time Series Analysis: Methods and Applications. ed. / Tata Subba Rao. Vol. 30 Amsterdam : Elsevier B.V., 2012. p. 157-186 (Handbook of Statistics; Vol. 30).

Research output: Chapter in Book/Report/Conference proceedingChapter

Hörmann, S & Kokoszka, PP 2012, Functional Time Series. in TS Rao (ed.), Time Series Analysis: Methods and Applications. vol. 30, Handbook of Statistics, vol. 30, Elsevier B.V., Amsterdam, pp. 157-186. DOI: 10.1016/B978-0-444-53858-1.00007-7
Hörmann S, Kokoszka PP. Functional Time Series. In Rao TS, editor, Time Series Analysis: Methods and Applications. Vol. 30. Amsterdam: Elsevier B.V.2012. p. 157-186. (Handbook of Statistics). Available from, DOI: 10.1016/B978-0-444-53858-1.00007-7
Hörmann, Siegfried ; Kokoszka, Piotr P./ Functional Time Series. Time Series Analysis: Methods and Applications. editor / Tata Subba Rao. Vol. 30 Amsterdam : Elsevier B.V., 2012. pp. 157-186 (Handbook of Statistics).
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