分野別セミナー

In this presentation, we discuss cyclic seasonal long-memory functional time series. A semiparametric Gegenbauer-type model is considered. Estimates for the singularity location and long-memory parameters based on general filter transforms are proposed. These transformations include wavelet transformations as a particular case. It is proven that the estimates converge almost surely to the true parameter values. The asymptotic normality of the estimators is also established. Solutions to the estimation equations are studied, and adjusted statistics are proposed. Similar results also apply to discretely sampled time series. Numerical results are presented to confirm the theoretical findings.
The talk is based on joint results with Prof. A.Ayache and M.Fradon (Université de Lille, France)