Nonparametric volatility estimation in scalar diffusions: Optimality\n across observation frequencies

2015/07/25 by Jakub Chorowski, Chorowski, Jakub
Economics, Econometrics and Finance · Mathematics · #60J60 #62M15 #Applications (stat.AP) #FOS: Computer and information sciences #FOS: Mathematics #Primary 62M05 #Probability (math.PR) #Statistical Methods and Inference #Stochastic processes and financial applications #secondary 62G99

paper · pdf · doi:10.48550/arxiv.1507.07139

openalex publication_date 2015/07/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The nonparametric volatility estimation problem of a scalar diffusion process\nobserved at equidistant time points is addressed. Using the spectral\nrepresentation of the volatility in terms of the invariant density and an\neigenpair of the infinitesimal generator the first known estimator that attains\nthe minimax optimal convergence rates for both high and low-frequency\nobservations is constructed. The proofs are based on a posteriori error bounds\nfor generalized eigenvalue problems as well as the path properties of scalar\ndiffusions and stochastic analysis. The finite sample performance is\nillustrated by a numerical example.\n

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