Adaptive estimation for Weakly Dependent Functional Times Series

2024/03/20 by Hassan Maissoro, Maissoro, Hassan, Valentin Patilea +3
Computer Science · Economics, Econometrics and Finance · Mathematics · #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #Time Series Analysis and Forecasting

paper · pdf · doi:10.48550/arxiv.2403.13706

openalex publication_date 2024/03/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01

Abstract

The local regularity of functional time series is studied under L^p-m-appro\-ximability 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 and the design, which can be sparse or dense. We also derive the asymptotic normality of the mean estimator, which allows honest inference for irregular mean functions. Simulations and a real data application illustrate the performance of the new estimators.

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