BIRS Workshop Lecture Videos

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BIRS Workshop Lecture Videos

Maximum autocorrelation factors for function-valued spatial/temporal data Shang, Han Lin


Dimension reduction techniques play a very important role in analyzing a set of functional data that possess temporal or spatial dependence. Of these dimension reduction techniques, functional principal components (FPCs) analysis remains as a popular approach that extracts 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 in a functional data set. Functional maximum autocorrelation factors (FMAFs) are proposed for modelling and forecasting a temporal/spatially dependent functional data. FMAFs find linear combinations of original functional data that have maximum autocorrelation and are decreasingly predictable functions of time. We show that FMAFs can be obtained by searching for the rotated components that have smallest integrated first derivatives. Through a basis function expansion, a set of scores are obtained by multiplying extracted FMAFs with original functional data. Then, these scores are forecast using a vector autoregressive model under stationarity. Conditional on fixed FMAFs and observed functional data, the point forecasts are obtained by multiplying forecast scores with FMAFs. Interval forecasts can also be obtained by forecasting bootstrapped FMAF scores. Through a set of Monte Carlo simulation results, we study the finite-sample properties of the proposed FMAFs. Wherever possible, we compare the performance between the FMAFs and FPCs. Presentor: Han Lin Shang (co-authored with Giles Hooker and Steven Roberts)

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