Time Series and Neural Networks Comparison on Gold, Oil, and the Euro A.G. Malliaris, Mary Malliaris Loyola University Chicago School of Business Administration

Overview Gold, oil, and the euro are three very important economic markets We look at the inter-relationships among the price behavior of all three Methods: – Time-series – Neural Networks

Problem Gold and oil have played important roles historically but have been studied independent of one another. Gold has served as the anchor of the Global Monetary System known as the Gold Standard. Since the introduction of the euro, and especially during the past few years, the euro, gold and oil appear to be interrelated.

Oil, gold and the euro as assets follow random walks and are cointegrated. Time series properties have emerged between these three markets the last few years This allows one to develop forecasting models using neural networks to predict one market using past information from the same and the other two markets.

Data and Methodology We use daily futures settlement prices measured in dollars for gold, oil, and the euro The data sample covers the time period from January 4, 2000 through December 31, 2007 There are a total of 1,991 observations for prices for each of the three daily closing prices The inputs are the lagged natural logs for 5 days of the euro, gold, and oil

Logs of the Three Variables

Time Series Model Tests of Stationarity Tests of Cointegration – Cointegration represents a long-run equilibrium relationship between two variables. – oil, gold and the euro are integrated of order one

Time Series Results The time series results imply that – oil adjusts to gold – the euro and oil have equal affects on each other – the weakest relationship is between gold and the euro

Augmented Dickey-Fuller Tests of Stationary

Time-Series Results The t-statistics indicate that the relationship between gold and oil is the strongest although the two markets move together oil adjusts to gold. Oil and the euro have a long-run equilibrium relationship without any one market being the driving force. The weakest relationship is between gold and the euro with minor evidence that increases in gold generate increases in the euro.

NN Variable Importance Clementine lists the variables by order of relative importance to the model, determined by which led to the greatest reduction in output variance. LEuro LGold LOil LEuroM LEuroM LEuroM LEuroM LEuroM LGoldM LGoldM LGoldM LGoldM LGoldM LOilM LOilM LOilM LOilM LOilM

Neural Network Results The neural network indicates that – oil impacts gold more than gold impacts oil – oils affect on the euro is greater than the euros effect on oil – golds impact on the euro is greater and faster than the euros impact on gold