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Title: Spectral analysis of high-dimensional functional time series Authors:  Xinghao Qiao - London School of Economics (United Kingdom)
Yirui Liu - London School of Economics (United Kingdom) [presenting]
Abstract: Statistical modeling for high-dimensional functional time series has attracted increasing attention in recent years. Under such a scenario, not only the number of functional variables, $p$, is large compared to the number of functional observations, $n$, but each function itself is infinite-dimensional with temporal dependence across observations. A useful approach to handle multivariate stationary functional times series by estimating its spectral density matrix function based on the averaged periodogram. We present a non-asymptotic theory for such spectral analysis. In particular, we derive useful concentration bounds on estimated spectral density matrix functions, which serves as a fundamental tool for further consistency analysis in large p, small n settings. We illustrate the usefulness of our derived concentration results in two examples. The first example considers the regularized estimation of high-dimensional spectral density matrix functions via functional thresholding. The second example considers a dynamic functional principal component analysis (FPCA), which is the main dimension reduction technique to handle functional time series. We rely on our developed concentration results to investigate the consistency properties of estimated terms for both examples under high dimensional scaling $\log(p/n)$ goes to zero.