Maximal autocorrelation factors for function-valued spatial/temporal data

Giles Hooker, Steven Roberts, Hanlin Shang

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

    Abstract

    Dimension reduction techniques play a key role in analysing 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 publicationMODSIM2015, 21st International Congress on Modelling and Simulation. Modelling and Simulation Society of Australia and New Zealand
    EditorsWeber, T., McPhee, M.J. and Anderssen, R.S.
    Place of PublicationAustralia
    PublisherThe Modelling and Simulation Society of Australia and New Zealand Inc.
    Pages159-164
    EditionPeer Reviewed
    ISBN (Print)9780987214355
    DOIs
    Publication statusPublished - 2015
    Event21st International Congress on Modelling and Simulation (MODSIM2015) - Gold Coast, Australia
    Duration: 1 Jan 2015 → …
    http://www.mssanz.org.au/modsim2015/index.html

    Conference

    Conference21st International Congress on Modelling and Simulation (MODSIM2015)
    Country/TerritoryAustralia
    Period1/01/15 → …
    OtherNovember 29-December 4 2015
    Internet address

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