The Application of Spectral Analysis to Demonstrate the Stochastic Distortion in the Delta Midrange of Price Series

Statistical analyses of price series generated by auction markets has been oriented historically toward the detection of structure (or lack of structure). While the results of such studies have been mixed, insufficient empirical evidence has been obtained on the properties of the measures employed to capture the inherent behavior of the price series. The first differences of the closing price have been shown, theoretically, to be unbiased for a random walk process. The use of averages, particularly the first differences of the midrange, has been shown to introduce spurious serial dependence in mathematical time series. It is the purpose of this article to examine the properties of both the delta close and delta midrange as measures, and to perform a variety of statistical tests and analyses to establish empirically the relationship between them. The predominant effort in seeking this relationship consisted of the spectral analysis of 11 years of May potato futures prices. The results obtained support the contention that the delta midrange amplifies the delta close, and that the amount of amplification is stochastic distortion in the delta midrange.