Instructors
Per Mykland and Lan Zhang.
About
The course is an introduction to the statistical analysis of high frequency (and sometimes high dimensional) financial data. Financial prices are often modeled as semi-martingales. We show how to use high frequency data to estimate volatility and quantities such as regression coefficients and leverage effect (skewness).
A selected reading list for the course includes part of the following sources:
It will not be possible to cover all this material fully, but we will select important highlights.
With adaptation, the methods may apply to other areas that have high frequency data (such as survival analysis, neural science and internet data).
Requirements
The course interfaces with several areas of study, and it will be helpful (but not required) to have a statistics course before taking this course. To keep the course free from too many requirements, we will review some of these interfaces: basic statistics (about one hour), time series (3-5 hours) and stochastic calculus (3-4 hours).
Structure
The plan for the course is roughly as follows:
- Day 1: Overview of high frequency data. Reminder of some basic statistics. Parametric inference for high frequency data.
- Day 2: Highlights of stochastic calculus.
- Day 3: Nonparametric assessment of variance in volatility estimators.
- Day 4: Asymptotics to estimate standard error in nonparametric estimators based on high frequency data. Stable convergence. Estimation with endogenous sampling times, and how to correct asymptotic bias.
- Day 5: Stock prices with noise: Microstructure noise in the semi-martingale model. Two scales realised volatility and pre-averaging, and how to combine them. Algebraic methods.
- Day 6: Time series, ARMA processes. Statistical arbitrage. Cointegration.
- Day 7: Multiple and high dimensions. Estimation of covariance. Principal component and factor analysis. Skewness, leverage effect.
If there is time, we will also cover contiguity and/or the concept of "observed asymptotic variance".