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Forecasting functional time series. (English) Zbl 1293.62267
Summary: We propose forecasting functional time series using weighted functional principal component regression and weighted functional partial least squares regression. These approaches allow for smooth functions, assign higher weights to more recent data, and provide a modeling scheme that is easily adapted to allow for constraints and other information. We illustrate our approaches using age-specific French female mortality rates from 1816 to 2006 and age-specific Australian fertility rates from 1921 to 2006, and show that these weighted methods improve forecast accuracy in comparison to their unweighted counterparts. We also propose two new bootstrap methods to construct prediction intervals, and evaluate and compare their empirical coverage probabilities.

MSC:
62P25 Applications of statistics to social sciences
62H25 Factor analysis and principal components; correspondence analysis
62G08 Nonparametric regression and quantile regression
62G09 Nonparametric statistical resampling methods
62J07 Ridge regression; shrinkage estimators (Lasso)
91D20 Mathematical geography and demography
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