Causalité de Granger pour des signaux à valeurs fonctionnelles
Résumé
Granger causality is an answer to knowing whether a signal influences another signal or not. Its principle relies on prediction theory: a first signal causes a second one if the first helps in the prediction of the second. Granger causality was developed for economy applications but is now widely used across many fields, however in stationary situations. Possible extension have already been proposed to tackle nonstationarity, but these are ratherad-hoc. A general theory for Granger causality in nonstationary contexts is still lacking. Motivated by cyclostationary signals, we propose here to model signals as discrete time signals taking values in infinite dimensional Hilbert function spaces. We then extend Granger causality in this particular context, providing strong and weak definitions, and giving some hints to practically apply the theory
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