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Title: Sieve bootstrap for high-dimensional time series Authors:  Daning Bi - The Australian National University (Australia) [presenting]
Yanrong Yang - The Australian National University (Australia)
Abstract: A bootstrap procedure for high dimensional time series based on the method of sieves is proposed which applies a low dimensional factor process to the high dimensional time series and then generates a residual-based bootstrap replicates of the low dimensional factor process. In particular, we develop a bootstrap approach which works properly when the dimension of time series N is as large as, or even larger than, the length of observed time series T. The first step of our method is applying a dimension reduction method, where we used a lower-dimensional factor process, to find a low dimension representation of the original time series. Then we can find a bootstrap replicates of the factor process based on a sieve method. And finally we can use the bootstrapped samples to create the prediction intervals of the process and study the statistical inference of a statistics of the original high dimensional time series. We show its consistency for bootstrapped mean vectors. A simulation study is performed to illustrate the coverage probabilities of the confidence band for mean vectors and the prediction intervals for the forecasts.