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Title: Sieve bootstrap for functional time series Authors:  Efstathios Paparoditis - University of Cyprus (Cyprus) [presenting]
Abstract: A new bootstrap procedure for functional time series is proposed which exploits a basic representation of the vector time series of Fourier coefficients appearing in the Karhunen-Loeve expansion of the functional process. A double, sieve-type bootstrap method to generate functional pseudo-time series is developed, which uses a finite set of functional principal components to capture the essential driving parts of the infinite dimensional process and a finite order parametric process to mimic the temporal dependence structure of the corresponding vector time series of Fourier coefficients. By allowing the number of functional principal components as well as the order of the model used to increase to infinity (at an appropriate rate) as the sample size increases, consistency of the sieve bootstrap procedure for a wide range of statistics is established. Some interesting applications in the context of variance estimation, fully functional testing and the construction of prediction intervals are discussed. An automatic data-driven method to select the bootstrap parameters is also proposed. In this context, a new variance-ratio criterion is used which explicitly takes into account the dependence of the functional time series. Some numerical examples illustrate the finite sample performance of the new bootstrap methodology proposed.