2004 NESS KEYNOTE SPEAKERS GEORGE COBB AND ANDREW LO
Is the Mathematical Statistics Course in a Vegetative State?
George W. Cobb
Department of Mathematics and Statistics
Mount Holyoke College
The future of the statistics profession depends on success in recruiting students to our subject. There will always be a need for statistics, of course, but there is a growing risk that the work of statistics will be taken over by people who think of themselves not as statisticians but as molecular biologists, market researchers, computer scientists, and others who specialize in any of the applied fields that use statistics.
What all these applications of statistics have in common, the glue that holds our universe together, is a reliance on mathematical models of uncertainty. Even as statistics has expanded the breadth and value of its achievements in applied areas, the core of our subject remains mathematical, and our future depends on attracting mathematically talented students. At most undergraduate colleges, the burden of doing that attracting falls to the mathematical statistics course, a course that has changed very little in half a century, despite extraordinary changes in the practice of statistics.
In my talk I will offer some criticisms of the traditional math stat course, and suggest some remedies and alternatives.
Temporal Averaging and Nonstationarities in Financial Markets
A common practice among quantitative financial analysts for dealing with non-stationary time series is to apply an exponentially declining weighting scheme to the data so that more distant observations are given less weight than more recent observations. We show that this practice of temporal averaging is incorrect for all but linear estimators, implying that variances, covariances, betas, Sharpe ratios, Value-at-Risk, and many other common financial statistics are incorrectly estimated with exponentially weighted time series. We propose an alternative approach to temporal averaging that yields unbiased estimators under the null hypothesis of independently and identically distributed observations, and which has attractive asymptotic properties under several stationary and nonstationary alternative hypotheses. Using this approach, we derive temporally averaged estimators for all the usual financial statistics and apply them to recent historical stock market data to demonstrate their empirical properties.