H. E. Stanley

Scaling of the distribution of price fluctuations of individual companies.

We present a phenomenological study of stock price fluctuations of individual companies. We systematically analyze two different databases covering securities from the three major U.S. stock markets: (a) the New York Stock Exchange, (b) the American Stock Exchange, and (c) the National Association of Securities Dealers Automated Quotation stock market. Specifically, we consider (i) the trades and quotes database, for which we analyze 40 million records for 1000 U.S. companies for the 2-yr period 1994-95; and (ii) the Center for Research and Security Prices database, for which we analyze 35 million daily records for approximately 16,000 companies in the 35-yr period 1962-96. We study the probability distribution of returns over varying time scales Delta t, where Delta t varies by a factor of approximately 10(5), from 5 min up to approximately 4 yr. For time scales from 5 min up to approximately 16 days, we find that the tails of the distributions can be well described by a power-law decay, characterized by an exponent 2.5 < proportional to < 4, well outside the stable Lévy regime 0 < alpha < 2. For time scales Delta t >> (Delta t)(x) approximately equal to 16 days, we observe results consistent with a slow convergence to Gaussian behavior. We also analyze the role of cross correlations between the returns of different companies and relate these correlations to the distribution of returns for market indices.

Inverse cubic law for the distribution of stock price variations

Abstract:The probability distribution of stock price changes is studied by analyzing a database (the Trades and Quotes Database) documenting every trade for all stocks in three major US stock markets, for the two year period January 1994 - December 1995. A sample of 40 million data points is extracted, which is substantially larger than studied hitherto. We find an asymptotic power-law behavior for the cumulative distribution with an exponent

Fractal mechanisms and heart rate dynamics: Long-range correlations and their breakdown with disease*

a \approx 3

Detrended cross-correlation analysis for non-stationary time series with periodic trends

, well outside the Lévy regime

Neurotoxic effects of thioflavin S-positive amyloid deposits in transgenic mice and Alzheimer's disease

(0 < \alpha < 2)

Sleep-wake differences in scaling behavior of the human heartbeat: Analysis of terrestrial and long-term space flight data

.