ABSENCE OF 1/f SPECTRA IN DOW JONES DAILY AVERAGE

Abstract

The power spectrum of the daily Dow Jones industrial average is calculated. It has been shown that the spectrum is P(f) ~1/f1.8, very close to that of the random walk series (1/f2 noise). In contrast to some previous belief, the Dow Jones index as well as other stock prices time series are not 1/f noise. The distribution of the daily change of the Dow Jones industrial average is also calculated. Several fittings of the distribution are carried out (for both the price change and the logarithm of the price change). It has been observed that the occurrence of the big loss on Black Monday (negative change of 508) does not fit the distribution of the smaller price fluctuations (e.g., smaller than 100). This lack of scaling for the frequency of occurrence from the large stock price losses to small price fluctuations can be compared with the much better scaling law in the frequency of occurrence for global earthquakes.