Recent years have seen an explosion in the availability and size of data in many areas of endeavor; the phenomenon is often referred to as big data. This project is concerned with a particular form of such data, namely high frequency data (HFD), where series of observations can see new data to arrive in fractions of milliseconds. HFD occurs in medicine, in finance and economics, in certain recordings relating to the environment, and perhaps in other areas. Research is often concerned with how to turn this data into knowledge, and this is where the current project will help. Specifically, the project has discovered a new way to look at the dependence relationships between the parameters governing the state of the HFD system. The new dependence structure permits the borrowing of information from adjacent time periods, and also from other series if one has a panel of data. The consequences of this new approach are being explored by the project. The research produces transformational improvements in the statistical handling of high frequency data.
The new way to look at dependence involves the representation of series of ordinary integrals with the help of stochastic integrals. This permits the use of high frequency regression techniques to connect the information in adjacent time intervals. It is achieved without altering current models. This has far-reaching consequences, leading to more efficient estimators, better prediction, and, in terms of accuracy, a more systematic treatment of the estimation of standard errors. Model selection will also be greatly facilitated. The methodology does not depend on either time or panel size being large; neither does it depend on assumptions such as stationarity of the data series. All the new dependence relationships can be consistently estimated from high frequency data inside the relevant time periods. Efficiency gains are at the very least close to 50%, and thus existing efficiency bounds will become irrelevant. It is expected that this approach will form a new paradigm for high frequency data. In addition to developing a general theory, the project is concerned with applications to financial data. Applied quantities of interest include realized daily volatility, correlations, leverage effect, volatility risk, fraction of jumps, and so on. We also work on applications to risk management, forecasting, and portfolio management. More precise estimators, with improved standard errors, will be useful in all these areas of finance. The results are of interest to main-street investors, regulators and policymakers, and the results are entirely in the public domain. The dependence structure also has application in other areas of research that have high frequency data, including medicine, neural science, and turbulence.
