Stock Market Data Example
Mandelbrot (1963) suggested that speculative price returns could be modeled by stable distributions. In his example he used logarithmic returns of cotton prices. The example that follows demonstrates the same principles with more than a century of daily closing prices of the Dow Jones Industrial Average. In the analysis, the unit of time is considered to be the trading day. It is not of consistent length, for instance the markets were closed for 4.5 months during 1914, for 11 days in 1933, and for a week in 2001. Furthermore the stocks within the average have changed a number of times, nevertheless the example shows that stable distributions can reasonably model logarithmic returns of stock market prices. An updated data set can be downloaded from the Dow Jones website, it starts on May 26, 1896. The data set used below runs through February 27, 2004.
The log[price] plot shows the price differences more clearly. It is the difference of the logarithm of price that exhibits stable behavior.
