
Bootstrap Prediction Bands for Functional Time Series
A bootstrap procedure for constructing pointwise or simultaneous predict...
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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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Statistical Inference for High Dimensional Panel Functional Time Series
In this paper we develop statistical inference tools for high dimensiona...
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Functional delta residuals and applications to functional effect sizes
Given a functional central limit (fCLT) and a parameter transformation, ...
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A Conformal Prediction Approach to Explore Functional Data
This paper applies conformal prediction techniques to compute simultaneo...
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The bootstrap in kernel regression for stationary ergodic data when both response and predictor are functions
We consider the double functional nonparametric regression model Y=r(X)+...
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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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Simultaneous predictive bands for functional time series using minimum entropy sets
Functional Time Series are sequences of dependent random elements taking values on some functional space. Most of the research on this domain is focused on producing a predictor able to forecast the value of the next function having observed a part of the sequence. For this, the Autoregresive Hilbertian process is a suitable framework. We address here the problem of constructing simultaneous predictive confidence bands for a stationary functional time series. The method is based on an entropy measure for stochastic processes, in particular functional time series. To construct predictive bands we use a functional bootstrap procedure that allow us to estimate the prediction law through the use of pseudopredictions. Each pseudorealisation is then projected into a space of finite dimension, associated to a functional basis. We use Reproducing Kernel Hilbert Spaces (RKHS) to represent the functions, considering then the basis associated to the reproducing kernel. Using a simple decision rule, we classify the points on the projected space among those belonging to the minimum entropy set and those that do not. We push back the minimum entropy set to the functional space and construct a band using the regularity property of the RKHS. The proposed methodology is illustrated through artificial and realworld data sets.
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