WIAS Preprint No. 911, (2004)

Nonparametric volatility estimation on the real line from low-frequency data


  • Reiß, Markus

2010 Mathematics Subject Classification

  • 62M05 60H10


  • diffusion process, nonparametric inference, wavelet, spectral approximation, low-frequency observations


We estimate the volatility function of a diffusion process on the real line on the basis of low frequency observations. The estimator is based on spectral properties of the estimated Markov transition operator of the embedded Markov chain. Asymptotic risk estimates for a growing number of observations are provided without assuming the observation distance to become small.

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