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Daily Speculations The Web Site of Victor Niederhoffer & Laurel Kenner Dedicated to the scientific method, free markets, deflating ballyhoo, creating value, and laughter; a forum for us to use our meager abilities to make the world of specinvestments a better place. |
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2/18/2005
A Philosophical Question, by Philip J. McDonnell
Much of my research has recently focused on developing methods to predict shorter term market moves on the order of one to 10 days. In reviewing the results a curious pattern emerged. The variables with the highest correlations with the market seemed to show weaker results when tested as trading systems. By contrast variables with near zero correlations often showed dramatic results when used as threshold variables.
A threshold variable would be something like:
If the S&P yesterday was up more than 1% use the actual value otherwise use zero (ignore the data)
In this case the threshold value would be +1%. One way to view this oddity is that the high correlations indicate a strong linear relationships. The threshold variables may indicate a non-linear relationship or possibly one which only comes into play when a threshold is surpassed.
One theory as to why this may be happening is that the rise of all the statarb shops has milked out most of the excess profits from simple linear correlations. Corresponding to this is that linear relationships are the easiest to understand and identify because the statistics are universally available. By contrast the threshold variable methodology may be little used and certainly requires a bit more thought as well as deciding on or "fitting" a threshold value.
Another theory is that the market is fundamentally non-linear. If so, attempts to predict its behavior with linear models and techniques will at best prove weak. This may explain why the market appears so random to its linear thinking human participants. To the extent this theory applies then the most fertile ground to hoe will be in the area of non-linear models.