Autoregressive forecasting of some functional climatic variations (Q2711683)

A function-valued time series \(y_1(t)\), \(y_2(t)\),\dots, \(y_n(t)\) 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 NEWLINE\[NEWLINE\hat\rho_h=\sum_{i=1}^{n-1} y_{i+1} K(\|y_i-y\|_{L_2}/h)\{\sum_{i=1}^{n-1} K(\|y_i-y\|_{L_2}/h)\}^{-1},NEWLINE\]NEWLINE 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.