Statistical Analysis of Price Series Obscured by Averaging Measures

Abstract

When measures such as the average or the midrange are used to report a typical value for the price series in each interval, the stochastic character of the underlying price process is subtly transformed. Fortunately, the spurious serial dependence introduced by averaging measures is sufficiently well understood to allow direct tests of many hypotheses to be made from averaged data. Moreover, a simple autoregressive transformation of the averaged data can be used to unscramble the effects of averaging on the lower-frequency components of the spectrum of the underlying process. These statistical devices are presented and are then illustrated by applications to the Cowles Commission Common- Stock Indexes, a massive collection of New York Stock Exchange price indexes tabulated in the form of monthly midranges.