Publications

2024

1. 

   Adaptive estimation for Weakly Dependent Functional Times Series

   Hassan Maissoro, Valentin Patilea, and Myriam Vimond

   arXiv preprint arXiv:2403.13706, 2024

   Abs arXiv PDF Poster Slides

   We study the local regularity of weakly dependent functional time series, under L^p-m-approximability assumptions. The sample paths are observed with error at possibly random, design points. Non-asymptotic concentration bounds of the regularity estimators are derived. As an application, we build nonparametric mean and autocovariance functions estimators that adapt to the regularity of the sample paths and the design which can be sparse or dense. We also derive the asymptotic normality of the adaptive mean function estimator which allows for honest inference for irregular mean functions. An extensive simulation study and a real data application illustrate the good performance of the new estimators.

2. 

   Adaptive estimation for Weakly Dependent Functional Times Series (Supplementary Material)

   Hassan Maissoro, Valentin Patilea, and Myriam Vimond

   2024

   Abs PDF

   In this supplement we provide the proofs of the lemmas and additional technical statements given in the Appendix of the main document. We also provide further empirical results and details on the construction of our simulation setups and the real data case. In section S.1 the proofs of the technical lemmas stated in the Appendix section A are given. Additional results for the local regularity estimation in the case of differentiable sample paths are stated and proved in section S.2. The proof of the lemmas used in the Appendix section C are given in section S.3 below. Details of the simulation setups, additional simulation results and insight on the choice of the tuning parameters involved in the local regularity estimation are given in section S.4.

3. 

   Adaptive prediction for Functional Times Series

   Hassan Maissoro, Valentin Patilea, and Myriam Vimond

   Work in progress, 2024

   Abs PDF Slides

   An adaptive procedure for curve prediction for a stationary functional time series is proposed. The sample paths of the functional times series are assumed to be irregular and are observed with error at discrete times in the domain. Our linear predictor is based on the best linear unbiased predictor (BLUP) and on the adaptive nonparametric mean and autocovariance functions estimators. That is, the bandwidth parameters of these estimators are chosen adaptively with respect to the local regularity of the sample paths. The benefit of such a procedure will be a reduction in risk prediction compared to existing procedures.