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We propose a new concept of modulated bipower variation for diffusion models with microstructure noise. We show that this method provides simple estimates for such important quantities as integrated volatility or integrated quarticity. Under mild conditions the consistency of modulated bipower variation is proven. Under further assumptions we prove stable… (More)

We consider a new class of estimators for volatility functionals in the setting of frequently observed Itō diffusions which are disturbed by i.i.d. noise. These statistics extend the approach of pre-averaging as a general method for the estimation of the integrated volatility in the presence of microstructure noise and are closely related to the original… (More)

Properties of a specification test for the parametric form of the variance function in diffusion processes dXt = b (t,Xt) dt + σ (t,Xt) dWt are discussed. The test is based on the estimation of certain integrals of the volatility function. If the volatility function does not depend on the variable x it is known that the corresponding statistics have an… (More)

- Kim Christensen, Mark Podolskij, Mathias Vetter
- J. Multivariate Analysis
- 2013

This paper presents a Hayashi-Yoshida type estimator for the covariation matrix of continuous Itô semimartingales observed with noise. The coordinates of the multivariate process are assumed to be observed at highly frequent nonsynchronous points. The estimator of the covariation matrix is designed via a certain combination of the local averages and the… (More)

- M. Vetter, G. Churkina, +9 authors C. Jones
- 2008

Globally, the year 2003 is associated with one of the largest atmospheric CO2 rises on record. In the same year, Europe experienced an anomalously strong flux of CO2 from the land to the atmosphere associated with an exceptionally dry and hot summer in Western and Central Europe. In this study we analyze the magnitude of this carbon flux anomaly and key… (More)

- M. Jung, G. Le Maire, +6 authors M. Reichstein
- 2007

Assessing the ability of three land ecosystem models to simulate gross carbon uptake of forests from boreal to Mediterranean climate in Europe M. Jung, G. Le Maire, S. Zaehle, S. Luyssaert, M. Vetter, G. Churkina, P. Ciais, N. Viovy, and M. Reichstein Max Planck Institute for Biogeochemistry, Jena, Germany International Max Planck Research School on Earth… (More)

- Kim Christensen, Mark Podolskij, Mathias Vetter
- Finance and Stochastics
- 2009

Market microstructure noise is a challenge to high-frequency based estimation of the integrated variance, because the noise accumulates with the sampling frequency. This has lead to widespread use of constructing the realized variance, a sum of squared intraday returns, from sparsely sampled data, for example 5or 15minute returns. In this paper, we analyze… (More)

- M. Vetter, G. Churkina, +15 authors M. Heimann
- 2007

Analyzing the causes and spatial pattern of the European 2003 carbon flux anomaly in Europe using seven models M. Vetter, G. Churkina, M. Jung, M. Reichstein, S. Zaehle, A. Bondeau, Y. Chen, P. Ciais, F. Feser, A. Freibauer, R. Geyer, C. Jones, D. Papale, J. Tenhunen, E. Tomelleri, K. Trusilova, N. Viovy, and M. Heimann Max-Planck Institute for… (More)

In this paper we investigate the problem of measuring deviations from stationarity in locally stationary time series. Our approach is based on a direct estimate of the L2-distance between the spectral density of the locally stationary process and its best approximation by a spectral density of a stationary process. An explicit expression of the minimal… (More)

- Markus Bibinger, Mathias Vetter
- 2013

We consider estimation of the quadratic (co)variation of a semimartingale from discrete observations which are irregularly spaced under high-frequency asymptotics. In the univariate setting, results from Jacod (2008) are generalized to the case of irregular observations. In the two-dimensional setup under non-synchronous observations, we derive a stable… (More)