Seminarium Zespołu Matematyki Obliczeniowej i Analizy Dużych Zbiorów Danych
Dnia 19.12.2023 (wtorek) o godz. 12:15
w sali 304 (łącznik A3-A4)
dr Jean-Marc Freyermuth
(Aix-Marseille University, France)
Joint work with: Dehay, D. and Dudek, A.
wygłosi referat:
„Some contributions to harmonizable time series and their application in EEG data analysis”
Serdecznie zapraszamy!
Abstrakt:
Harmonizable time series are natural extensions of stationary time series with a spectral decomposition whose components are correlated. Thus, the covariance function of a harmonizable time series is bivariate and admits a two-dimensional Fourier decomposition (Loève spectrum). They form a broad class of nonstationary processes that has been subject of investigation for a long time, starting with Loève (1948-1963), Rozanov (1959) and Cramèr (1961). In this talk, we introduce a parametric form for these harmonizable processes, namely the Harmonizable Vector AutoRegressive and Moving Average models (HVARMA), and we give tools to generate finite time sample realizations of HVARMA with known Loève spectrum. Then, we discuss nonparametric estimation of spectral characteristics of spatiotemporal processes that are locally time-harmonizable, and we illustrate its application in EEG data analysis.
Dehay, D., Dudek, A., Freyermuth, J.-M. (2023). Spectral characteristics of Harmonizable VARMA time series. Preprint.
Aston, J., Dehay, D., Dudek, A., Freyermuth, J.-M., Szucs, D., Colling, L. (2023). Spectrum inference for replicated spatial locally time-harmonizable time series. Electronic journal of statistics, 17(1), 1371–1410.