Research Seminars

Microstructure Bias and Multiscale Inference

Professor Sofia Olhede
Department of Statistical Science, University College London

Tuesday 7 October 2008, 15:00, Room 105

Abstract

There are many instances where observed data possesses structure at many different characteristic length and time scales. As examples we mention data in atmosphere and ocean science where lack of high frequency resolution enforces the need to parameterise the high frequency structure, and also high-frequency financial data susceptible to market microstructure noise. Due to the complexity of the physical systems under investigation, it is often necessary to use simplified, coarse grained models that ignore the small scales. With improved measurement resolution it transpires that structure at very small scales is not consistent with the coarse grained models used to describe phenomena at longer scales. The effects of such microstructural behaviour on inference can be disastrous, leading in some cases to inconsistent estimation at decreasing sampling periods. Previous methods have dealt with this problem by subsampling to decrease resolution and remove the bias due to the microstructure. Such procedures may violate the principle that inferences should be based on the full set of observed data.

We focus on the estimation of the integrated volatility of a high frequency financial process. In this case the structure of the process is governed by a stochastic differential equation, and the observed process is contaminated by additive noise. We take a frequency domain approach and advocate inferring the degree of contamination directly from the data. Once the degree of contamination has been estimated, then this allows us to frequency-by-frequency correct the estimator of the integrated volatility and calculate a bias-corrected estimator. This procedure is fast, robust to different signal to microstructure scenarios, and is also easily extended to the problem of correlated microstructure noise. Theory can be developed as long as the sampled Ito process has harmonizable increments, and suitable dynamic spectral range.

This is joint work with Greg Pavliotis and Adam Sykulski (Imperial College London).