1. The Econometrics of High Frequency Financial Data: Models and Microstructure

Abstract: Recent years have seen a rapid growth in high frequency

financial data, This has opened the possibility of accurately

determining volatility in small time periods, such as one day. We

introduce the types of data, discuss what quantities can reasonably be

estimated in this setting, and review challenges for research.

A main issue in data analysis is microstructure noise. Recent work on

such estimation indicates that it is necessary to fit the data with a

hidden semi-martingale model, thereby incorporating the noise. We

develop the methodology for analyzing such data, including two- and

multi-scale sampling. We shall see that the resulting estimators have

the best possible rates of convergence, and characterize the

statistical error in estimators. We also show how to make these

estimators robust to dependent noise. We shall see that, in a sense,

the estimators automatically "clean" the data. The ideas of two scale

sampling also shed light on covariance estimation for non-synchronized

price series.

2. Between Data Cleaning and Inference: Pre-Averaging and other Robust

Estimators of the Efficient Price

Abstract: Pre-averaging is another popular strategy for mitigating

microstructure in high frequency financial data. As the term suggests,

transaction data (say) are averaged over short time periods ranging

from 30 seconds to five minutes, and the resulting averages

approximate the efficient price process much better than the raw data.

Apart from reducing the size of the microstructure, the methodology

also helps synchronize data from different securities. The procedure

is robust to short term dependence in the noise.

In this talk, we develop a general theory for pre-averaging-based

estimation. We show that, up to a contiguity adjustment, the

pre-averaged process behaves as if one sampled from a semimartingale

(with unchanged volatility) plus a Gaussian error. In fact, locally,

the return process becomes a Gaussian MA(1) process, thus enabling

some of the classical machinery.

Since averages can be subject to outliers, we have developed a broader

theory which also applies to cases where M-estimation is used to pin

down the efficient price in local neighborhoods. While the procedure

entails some information loss, we show that the procedure is

remarkably efficient. And the methodology applies off-the-shelf to any

high frequency econometric problem. Estimating the efficient price is

a form of pre-processing of the data, and hence also the methods in

this paper serve the purpose of data cleaning.