Statistical inference for high dimensional panel functional time series
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Date
2020
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Abstract
In this paper we develop statistical inference tools for high dimensional functional
time series. We introduce a new concept of physical dependent processes in
the space of square integrable functions, which adopts the idea of basis decomposition
of functional data in these spaces, and derive Gaussian and multiplier bootstrap
approximations for sums of high dimensional functional time series. These results
have numerous important statistical consequences. Exemplarily, we consider the development
of joint simultaneous confidence bands for the mean functions and the
construction of tests for the hypotheses that the mean functions in the spatial dimension
are parallel. The results are illustrated by means of a small simulation study
and in the analysis of Canadian temperature data.
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Keywords
high dimensional functional time series, physical dependence, Gaussian approximation, simultaneous confidence bands, hypotheses tests, spatio-temporal data