[Statlist] Research Seminar in Statistics *FRIDAY 8 OCTOBER 2021* GSEM, University of Geneva

[gsem-support-instituts]

Due to new measures decided by the Federal Council, all public events organized by the UNIGE are subject to the compulsory presentation of the COVID certificate


Dear All,

We are pleased to invite you to our next Research Seminar.

Looking forward to seeing you


Organizers :                                                                                   
E. Cantoni - S. Engelke - D. La Vecchia - E. Ronchetti
S. Sperlich - F. Trojani - M.-P. Victoria-Feser


FRIDAY 8 OCTOBER 2021 at 11:15am, Uni-Mail M 5220 & ONLINE

Zoom research webinar: https://unige.zoom.us/j/92924332087?pwd=U1U1NFk4dTFCRHBMeWYrSDBQcXBiQT09
Meeting ID: 929 2433 2087
Passcode: 399192


Factor Models for High-Dimensional Functional Time Series
(joint with Gilles Nisol (ULB) and Marc Hallin (ULB))
Shahin TAVAKOLI (https://www.unige.ch/gsem/en/research/faculty/all/shahin-tavakoli/) - GSEM, University of Geneva
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ABSTRACT:
We set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result stating that, under mild assumptions on the covariance operator of the cross-section, we can represent each FTS as the sum of a common component driven by scalar factors loaded via functional loadings, and a mildly cross-correlated idiosyncratic component. Our model and theory are developed in a general Hilbert space setting that allows for mixed panels of functional and scalar time series. We then turn to the identification of the number of factors, and the estimation of the factors, their loadings, and the common components. We provide a family of information criteria for identifying the number of factors, and prove their consistency. We provide average error bounds for the estimators of the factors, loadings, and common component; our results encompass the scalar case, for which they reproduce and extend, under weaker conditions, well-established similar results. Under slightly stronger assumptions, we also provide uniform bounds for the estimators of factors, loadings, and common component, thus extending existing scalar results. Our consistency results in the asymptotic regime where the number N of series and the number T of time observations diverge thus extend to the functional context the "blessing of dimensionality" that explains the success of factor models in the analysis of high-dimensional (scalar) time series. We provide numerical illustrations that corroborate the convergence rates predicted by the theory, and provide finer understanding of the interplay between N and T for estimation purposes. We conclude with an application to forecasting mortality curves, where we demonstrate that our approach outperforms existing methods.


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