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Autoregressive forecasting of some functional climatic variations. (English) Zbl 0962.62089
A function-valued time series $$y_1(t)$$, $$y_2(t)$$,…, $$y_n(t)$$ is considered where $$y_i$$ are observed at some fixed points $$t_j$$, $$j=1,\dots p$$. The paper is devoted to the problem of forecasting $$y_{n+s}(t)$$. The authors consider a functional kernel autoregression predictor $\hat\rho_h=\sum_{i=1}^{n-1} y_{i+1} K(\|y_i-y\|_{L_2}/h)\{\sum_{i=1}^{n-1} K(\|y_i-y\|_{L_2}/h)\}^{-1},$ a Hilbert space autoregression model FAR(1) and local FAR(1) which uses kernel-type localization techniques. Splines are used to approximate $$y_i$$ in unobservable points and cross-validation to select a bandwidth $$h$$. This technique is applied to the forecasting of climatological time-series describing the El-Niño southern oscillation effects.

##### MSC:
 62M20 Inference from stochastic processes and prediction 62P12 Applications of statistics to environmental and related topics 62M30 Inference from spatial processes 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
fda (R)
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