Articlebronze2010

Limit theorems for moving averages of discretized processes plus noise

Jean Jacod · Mark Podolskij · Mathias Vetter

98 citations0/0 files storedThe Annals of Statistics

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Stochastic processes and financial applications Financial Risk and Volatility Modeling Statistical Methods and Inference

Abstract

This paper presents some limit theorems for certain functionals of moving averages of semimartingales plus noise which are observed at high frequency. Our method generalizes the pre-averaging approach (see [Bernoulli 15 (2009) 634–658, Stochastic Process. Appl. 119 (2009) 2249–2276]) and provides consistent estimates for various characteristics of general semimartingales. Furthermore, we prove the associated multidimensional (stable) central limit theorems. As expected, we find central limit theorems with a convergence rate n−1/4, if n is the number of observations.

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References

2002Econometric Analysis of Realized Volatility and its Use in Estimating Stochastic Volatility Models 2005A Tale of Two Time Scales 2008Designing Realized Kernels to Measure the ex post Variation of Equity Prices in the Presence of Noise 2005How Often to Sample a Continuous-Time Process in the Presence of Market Microstructure Noise 2008Microstructure noise in the continuous case: The pre-averaging approach 2005Separating microstructure noise from volatility 2009Testing for jumps in a discretely observed process 2006Efficient estimation of stochastic volatility using noisy observations: a multi-scale approach

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