Correlation methods in the statistical analysis of financial trading data

Thesis

This thesis considers problems associated with the statistical analysis of correlation in financial trading data. Sources of data are identified and their characteristics are described. Nowadays most financial transactions are carried out electronically on automated exchanges or electronic communication networks and active participants in the market re- quire sophisticated computing infrastructure to compete effectively. These data are shown to present novel statistical challenges both in retrospectively analysing the vast stores of accumulated historical data and also in online processing of high-bandwidth multiple data streams arriving on millisecond time-scales. We show that computational speed dictates the range of statistical tools that are available for high-speed calculation.

The measurement and interpretation of correlation is a dominant concern in the analysis of high-frequency financial data. We compare and develop methods for assessing volatility, cross-asset correlation and lead-lag effects. For volatility estimation we consider a class of estimates that can accommodate noisy irregularly spaced data. We derive explicit expressions for the variance of these estimators and show how the estimators can be modified to obtain infill consistency. We then consider the problem of covariance estimation and develop a new estimator, demonstrating its superior performance. We explore the problems of quantifying lead-lag relationships and show that our new covariance estimator provides a sharper estimate of lead-lag delay. We then develop a method of exploring lead-lag structure in depth and demonstrate how to obtain a maximum likelihood estimator of the delay structure. The final chapter briefly describes ongoing research questions relating to the design of hedging strategies at times of market disruption.

Authors: Azzollini, Y

• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford
• Keywords: Trading Latency; Latency; Asynchronous correlation; High Frequency Trading; Big data; Correlation; High-Frequency Covariance Estimates With Noisy; Financial data; Asynchronous Financial Data; Statistical Learning; Machine Leaning; Correlation methods in the statistical analysis of financial trading data; Lagged correlation; Volatility
• Subjects: Trading Latency; Latency; Asynchronous correlation; High Frequency Trading; Big data; Correlation; High-Frequency Covariance Estimates With Noisy; Financial data; Asynchronous Financial Data; Statistical Learning; Machine Leaning; Correlation methods in the statistical analysis of financial trading data; Lagged correlation; Volatility