2017/06/27 by Rida Benhaddou, Benhaddou, Rida
Economics, Econometrics and Finance · Mathematics · #62G05 #62G08 #62G20 #FOS: Mathematics #Financial Risk and Volatility Modeling #Statistical Methods and Inference #Statistics Theory (math.ST) #Stochastic processes and financial applications
paper · pdf · doi:10.48550/arxiv.1706.08648
openalex publication_date 2017/06/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We investigate the problem of estimating a function f based on observations from its noisy convolution when the noise exhibits long-range dependence. We construct an adaptive estimator based on the kernel method, derive minimax lower bound for the L2-risk when f belongs to Sobolev space and show that such estimator attains optimal rates that deteriorate as the LRD worsens.