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Spectral estimation of the Lévy density in partially observed affine models. (English) Zbl 1216.62132

Summary: The problem of estimating the Lévy density of a partially observed multidimensional affine process from low-frequency and mixed-frequency data is considered. The estimation methodology is based on the log-affine representation of the conditional characteristic function of an affine process and local linear smoothing in time. We derive almost sure uniform rates of convergence for the estimated Lévy density both in mixed-frequency and low-frequency setups and prove that these rates are optimal in the minimax sense. Finally, the performance of the estimation algorithms is illustrated in the case of the Bates stochastic volatility model.

MSC:

62M05 Markov processes: estimation; hidden Markov models
60F15 Strong limit theorems
62P05 Applications of statistics to actuarial sciences and financial mathematics
60J25 Continuous-time Markov processes on general state spaces
91G70 Statistical methods; risk measures
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