Maximal autocorrelation factors for function-valued spatial/temporal data

G. Hooker, Steven Roberts, H. L. Shang*

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference proceeding contributionpeer-review

Abstract

Dimension reduction techniques play a key role in analyzing functional data that possess temporal or spatial dependence. Of these dimension reduction techniques functional principal components analysis (FPCA) remains a popular approach. Functional principal components extract a set of latent components by maximizing variance in a set of dependent functional data. However, this technique may fail to adequately capture temporal or spatial autocorrelation. Functional maximum autocorrelation factors (FMAF) are proposed as an alternative for modeling and forecasting temporally or spatially dependent functional data. FMAF find linear combinations of the original functional data that have maximum autocorrelation and that are decreasingly predictable functions of time. We show that FMAF can be obtained by searching for the rotated components that have the smallest integrated first derivatives. Through a basis function expansion, a set of scores are obtained by multiplying the extracted FMAF with the original functional data. Autocorrelation in the original functional time series is manifested in the autocorrelation of these scores derived. Through a set of Monte Carlo simulation results, we study the finite-sample properties of the proposed FMAF. Wherever possible, we compare the performance between FMAF and FPCA. In an enhanced vegetation index data from Harvard Forest we apply FMAF to capture temporal or spatial dependency.

Original languageEnglish
Title of host publicationMODSIM 2015
Subtitle of host publicationProceedings of the 21st International Congress on Modelling and Simulation
EditorsTony Weber, Malcolm McPhee, Robert Anderssen
Place of PublicationGold Coast
PublisherModelling and Simulation Society of Australia and New Zealand
Pages159-165
Number of pages7
ISBN (Electronic)9780987214355
DOIs
Publication statusPublished - 1 Jan 2015
Externally publishedYes
Event21st International Congress on Modelling and Simulation: Partnering with Industry and the Community for Innovation and Impact through Modelling, MODSIM 2015 - Held jointly with the 23rd National Conference of the Australian Society for Operations Research and the DSTO led Defence Operations Research Symposium, DORS 2015 - Broadbeach, Australia
Duration: 29 Nov 20154 Dec 2015

Conference

Conference21st International Congress on Modelling and Simulation: Partnering with Industry and the Community for Innovation and Impact through Modelling, MODSIM 2015 - Held jointly with the 23rd National Conference of the Australian Society for Operations Research and the DSTO led Defence Operations Research Symposium, DORS 2015
CountryAustralia
CityBroadbeach
Period29/11/154/12/15

Keywords

  • Autocorrelation operator
  • Functional time series
  • Linear dimension reduction technique
  • Spatially dependent functional data

Fingerprint Dive into the research topics of 'Maximal autocorrelation factors for function-valued spatial/temporal data'. Together they form a unique fingerprint.

Cite this