• Corpus ID: 88511823

Spectral covolatility estimation from noisy observations using local weights

@article{Bibinger2011SpectralCE,
  title={Spectral covolatility estimation from noisy observations using local weights},
  author={Markus Bibinger and Markus Rei{\ss}},
  journal={arXiv: Statistics Theory},
  year={2011}
}
We propose localized spectral estimators for the quadratic covariation and the spot covolatility of diffusion processes which are observed discretely with additive observation noise. The eligibility of this approach to lead to an appropriate estimation for time-varying volatilities stems from an asymptotic equivalence of the underlying statistical model to a white noise model with correlation and volatility processes being constant over small intervals. The asymptotic equivalence of the… 

Figures and Tables from this paper

OPTIMAL SPARSE VOLATILITY MATRIX ESTIMATION FOR HIGH-DIMENSIONAL ITÔ PROCESSES WITH MEASUREMENT ERRORS
TLDR
This paper investigates rate-optimal estimation of the volatility matrix of a high dimensional It^o process observed with measurement errors at discrete time points and constructs a volatility matrix estimator to achieve the optimal convergence rate.

References

SHOWING 1-10 OF 20 REFERENCES
Efficient Covariance Estimation for Asynchronous Noisy High‐Frequency Data
Abstract.  We focus on estimating the integrated covariance of log‐price processes in the presence of market microstructure noise. We construct a consistent asymptotically unbiased estimator for the
High-Frequency Covariance Estimates With Noisy and Asynchronous Financial Data
This article proposes a consistent and efficient estimator of the high-frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise.
Quasi-Maximum Likelihood Estimation of Volatility with High Frequency Data
This paper investigates the properties of the well-known maximum likelihood estimator in the presence of stochastic volatility and market microstructure noise, by extending the classic asymptotic
Asymptotic equivalence for inference on the volatility from noisy observations
We consider discrete-time observations of a continuous martingale under measurement error. This serves as a fundamental model for high-frequency data in finance, where an efficient price process is
Multivariate realised kernels: consistent positive semi-definite estimators of the covariation of equity prices with noise and non-synchronous trading
We propose a multivariate realised kernel to estimate the ex-post covariation of log-prices. We show this new consistent estimator is guaranteed to be positive semi-definite and is robust to
Efficient Estimation of Stochastic Volatility Using Noisy Observations: A Multi-Scale Approach
With the availability of high frequency financial data, nonparametric estimation of volatility of an asset return process becomes feasible. A major problem is how to estimate the volatility
A Tale of Two Time Scales
TLDR
Under this framework, it becomes clear why and where the “usual” volatility estimator fails when the returns are sampled at the highest frequencies, and a way of finding the optimal sampling frequency for any size of the noise.
How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise
TLDR
This work shows that the optimal sampling frequency at which to estimate the parameters of a discretely sampled continuous-time model can be finite when the observations are contaminated by market microstructure effects, and addresses the question of what to do about the presence of the noise.
...
...