An adaptive procedure for curve prediction for a stationary weakly dependent functional time series is proposed. The sample paths of the functional time series are assumed to be irregular and observed with error at discrete times within the domain. Our linear predictor is based on the best linear unbiased predictor (BLUP) and on the adaptive nonparametric mean and autocovariance functions estimators. In other words, the bandwidth parameters of these estimators are chosen adaptively according to the local regularity of the sample paths. We also construct prediction regions derived from our estimation procedure.
Key words: adaptive estimation; (auto-)covariance function; kernel smoothing; weak dependence |
