Functional stable limit theorems for quasi-efficient spectral covolatility estimators
| Autor: | Randolf Altmeyer, Markus Bibinger |
|---|---|
| Rok vydání: | 2015 |
| Předmět: |
Statistics and Probability
Multivariate statistics Mathematical optimization Applied Mathematics Estimator Spectral density estimation Mathematics - Statistics Theory 62G05 62G20 62M10 Statistics Theory (math.ST) Bivariate analysis Semimartingale Modeling and Simulation FOS: Mathematics Applied mathematics Volatility (finance) Smoothing Mathematics Central limit theorem |
| Zdroj: | Stochastic Processes and their Applications. 125:4556-4600 |
| ISSN: | 0304-4149 |
| Popis: | We consider noisy non-synchronous discrete observations of a continuous semimartingale with random volatility. Functional stable central limit theorems are established under high-frequency asymptotics in three setups: one-dimensional for the spectral estimator of integrated volatility, from two-dimensional asynchronous observations for a bivariate spectral covolatility estimator and multivariate for a local method of moments. The results demonstrate that local adaptivity and smoothing noise dilution in the Fourier domain facilitate substantial efficiency gains compared to previous approaches. In particular, the derived asymptotic variances coincide with the benchmarks of semiparametric Cram\'er-Rao lower bounds and the considered estimators are thus asymptotically efficient in idealized sub-experiments. Feasible central limit theorems allowing for confidence are provided. Comment: to appear, Stochastic Processes and their Applications, 2015 |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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