Here is an example from the S&P 500 (e-mini futures) last fall, using some of the techniques from Sherry's book.
- The graph across the top is the price.
- Histogram "N" is the 5 minute prices changes (histogram of first differences
- To the right of that is the differential spectrum test. It tells you if dependencies exist or not (but not what kind of dependencies). It tests for symmetry of the first-difference histogram.
- Directly under the differential spectrum test is the digram test for serial price dependency. "1" means price decrease and "2" means increase. So "11" means a decrease followed by a decrease, "12" means decrease then increase, etc. "obs" is how many were seen in this time series and "exp" is how many are expected from a random, independent time series.
- The two cdfs (cumulative distribution functions) plotted along the left-bottom are tests for stationarity (labelled stn) and randomness (labelled ran)
These results showed the price changes over 5 min intervals, for the S&P emini between Sept. 21 and Oct 14, were stationary, random, but dependent.
The dependency means that trends are in play and chart patterns can be useful. Random means that the historical prices don't completely determine the future prices. Good traders already knew all this.
But it's nice to see proof. Furthermore, you can watch the markets change their behavior and also see difference in time frames with this kind of analysis.
The problem, I found, with studying dependencies there are not many statisticians who study dependencies. Useful material is difficult to come by.