M. E. MalliarisLoyola University Chicago, mmallia@luc.edu

 S. G. Malliaris

Yale University, steven.malliaris@yale.edu

Crude oil Heating oil Gasoline Natural gas Propane

CL HO PN HU NG

CL 1 - - - -

HO 0.959721 1 - - -

PN 0.842248 0.881154 1 - -

HU 0.964905 0.926191 0.847288 1 -

NG 0.669869 0.731288 0.677979 0.657551 1

Daily Spot Prices Five Variables From Jan 3, 1994 and Dec 31, 2002 The input variables:

daily closing spot pricepercent change in daily closing spot price

from the previous daystandard deviation over the previous 5

trading daysStandard deviation over the previous 21

trading days

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.

Avg. Absolute Error Mean Squared Error

SimpleRegression

Neural Net Simple

Regression

Neural Net

CL 1.973 2.126 1.120 6.013 6.653 2.269

HO 0.051 0.055 0.035 0.004 0.005 0.002

HU 0.057 0.053 0.029 0.006 0.004 0.001

NG 0.388 0.414 0.218 0.240 0.242 0.075

PN 0.041 0.061 0.080 0.003 0.006 0.009

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