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High-dimensional functional time series forecasting: an application to age-specific mortality rates. (English) Zbl 1415.62093

Summary: We address the problem of forecasting high-dimensional functional time series through a two-fold dimension reduction procedure. The difficulty of forecasting high-dimensional functional time series lies in the curse of dimensionality. In this paper, we propose a novel method to solve this problem. Dynamic functional principal component analysis is first applied to reduce each functional time series to a vector. We then use the factor model as a further dimension reduction technique so that only a small number of latent factors are preserved. Classic time series models can be used to forecast the factors and conditional forecasts of the functions can be constructed. Asymptotic properties of the approximated functions are established, including both estimation error and forecast error. The proposed method is easy to implement, especially when the dimension of the functional time series is large. We show the superiority of our approach by both simulation studies and an application to Japanese age-specific mortality rates.

MSC:

62P10 Applications of statistics to biology and medical sciences; meta analysis
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M20 Inference from stochastic processes and prediction
62P25 Applications of statistics to social sciences
62N05 Reliability and life testing
62H25 Factor analysis and principal components; correspondence analysis

Software:

freqdom.fda; fda (R)
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References:

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