1. M. E. Malliaris Loyola University Chicago, mmallia@luc.edu S. G. Malliaris Yale University, steven.malliaris@yale.edu

2.  Crude oil  Heating oil  Gasoline  Natural gas  Propane

5. CLHOPNHUNG CL1---- HO0.9597211--- PN0.8422480.8811541-- HU0.9649050.9261910.8472881- NG0.6698690.7312880.6779790.6575511

6.  Daily Spot Prices  Five Variables  From Jan 3, 1994 and Dec 31, 2002  The input variables:  daily closing spot price  percent change in daily closing spot price from the previous day  standard deviation over the previous 5 trading days  Standard deviation over the previous 21 trading days

7.  Regression  Neural Network  Each neural network model used twenty-one inputs (the 20 original fields, plus the non- numeric cluster identifier), one hidden layer with twenty nodes, and one output node.

8. Avg. Absolute ErrorMean Squared Error Simple Regres sion Neural NetSimple Regres sion Neural Net CL1.9732.1261.1206.0136.6532.269 HO0.0510.0550.0350.0040.0050.002 HU0.0570.0530.0290.0060.0040.001 NG0.3880.4140.2180.2400.2420.075 PN0.0410.0610.0800.0030.0060.009

14.  There is enough information contained in a simple set of price data to allow effective forecasting  An ability to predict the price of a given source good does not necessarily imply an ability to predict the price of such a good’s byproducts  Traditional statistical techniques for understanding and extracting information about trends are often less than ideal in market situations