
Modelfree Bootstrap for a General Class of Stationary Time Series
A modelfree bootstrap procedure for a general class of stationary time ...
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Double bootstrapping for visualising the distribution of descriptive statistics of functional data
We propose a double bootstrap procedure for reducing coverage error in t...
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Simultaneous predictive bands for functional time series using minimum entropy sets
Functional Time Series are sequences of dependent random elements taking...
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DistributionFree Prediction Bands for Multivariate Functional Time Series: an Application to the Italian Gas Market
Uncertainty quantification in forecasting represents a topic of great im...
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The autoregression bootstrap for kernel estimates of smooth nonlinear functional time series
Functional times series have become an integral part of both functional ...
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Confidence surfaces for the mean of locally stationary functional time series
The problem of constructing a simultaneous confidence band for the mean ...
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Longterm prediction intervals with many covariates
Accurate forecasting is one of the fundamental focus in the literature o...
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Bootstrap Prediction Bands for Functional Time Series
A bootstrap procedure for constructing pointwise or simultaneous prediction intervals for a stationary functional time series is proposed. The procedure exploits a general vector autoregressive representation of the timereversed series of Fourier coefficients appearing in the KarhunenLoève representation of the functional process. It generates backwardsintime, functional replicates that adequately mimic the dependence structure of the underlying process and have the same conditionally fixed curves at the end of each functional pseudotime series. The bootstrap prediction error distribution is then calculated as the difference between the modelfree, bootstrapgenerated future functional observations and the functional forecasts obtained from the model used for prediction. This allows the estimated prediction error distribution to account for not only the innovation and estimation errors associated with prediction but also the possible errors from model misspecification. We show the asymptotic validity of the bootstrap in estimating the prediction error distribution of interest. Furthermore, the bootstrap procedure allows for the construction of prediction bands that achieve (asymptotically) the desired coverage. These prediction bands are based on a consistent estimation of the distribution of the studentized prediction error process. Through a simulation study and the analysis of two data sets, we demonstrate the capabilities and the good finitesample performance of the proposed method.
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