gold, oil and the euro: hypotheses, time series and neural network analysis for futures data a. g....
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GOLD, OIL AND THE EURO:HYPOTHESES, TIME SERIES AND NEURAL NETWORK ANALYSIS FOR FUTURES DATA
A. G. Malliaris and Mary E. Malliaris
Loyola University Chicago
ILLINOIS ECONOMICS ASSOCIATION
MEETINGS
October 16-17, 2009
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Outline• General Comments About Gold, Oil and
the Euro
• These Markets Prior to the Creation of the Euro
• How are these Markets Related Since the Creation of the Euro
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Gold
• As an Anchor of the Gold Standard
• As a Hedge Against Inflation
• As a Free Commodity Since mid-1971
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Long-Term Gold Price
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Oil
• Significant Commodity in Global Economy
• Its role today is somehow lesser than in early 70s but still important
• Extremely volatile
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Long-Term Oil Price
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The Euro
• Start with the European Common Market in 1957
• From a Customs Union to One Market
• One Market with One Currency
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The Creation of the Euro
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Data
Daily data from January 4, 2000 to
December 31, 2007 for a total of 1,991
observations from Barchart.
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Daily Data since 1999
0.00
1.00
2.00
3.00
4.00
5.00
6.00
7.00
8.00
-.3
-.2
-.1
0.00
0.10
0.20
0.30
0.40
0.50
Ln Oil
Ln Gold
Ln Euro
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Hypotheses
• Do these 3 Markets follow Random Walks?
• The twin U.S. deficits weaken the dollar and strengthen the euro and induce oil producers to demand compensation.
• Increases in oil prices impact gold prices.
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Time Series Methods
• Are the euro, oil and gold co-integrated?
• Are there any short- and long-term relationships between the euro, oil and gold?
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Augmented Dickey-Fuller Tests of Stationarity
• The model is:
T
iititt XcXataaX
11210
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Price Level (LN(X))
Only Lags Lags and Constant
Lags, Constant, and Trend
Gold
No lags 2.361111 0.667188 -2.836540
5 lags 2.363708 0.693961 -2.843861
20 lags 2.373704 0.766124 -2.862830
Oil
No lags 1.191509 -0.626496 -2.759707
5 lags 1.313748 -0.461972 -2.541877
20 lags 1.368074 -0.235474 -2.456710
Euro
No lags 0.631741 -0.079099 -3.034661
5 lags 0.659061 -0.049944 -3.063701
20 lags 0.521473 -0.293593 -2.657669
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First Price Differences (LN(Xt) - LN(Xt-1))
Only Lags Lags and Constant
Lags, Constant, and Trend
Gold
No lags -46.65579 -46.77877 -46.81729
5 lags -18.68709 -18.86720 -18.93417
20 lags -9.389532 -9.698579 -9.833956
Oil
No lags -45.22329 -45.25046 -45.24871
5 lags -19.52137 -19.57521 -19.58983
20 lags -10.21073 -10.31103 -10.35710
Euro
No lags -46.05127 -46.07716 -46.10367
5 lags -17.92471 -17.97228 -18.02022
20 lags -9.111516 -9.214248 -9.259299
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Engle and Granger Test of Cointegration of LN(Price)
Dependent Variable (X)
Independent Variable (Y)
b0 t-stat
Gold Oil -0.009211 -2.920998
Oil Gold -0.010399 -3.122336
Gold Euro -0.003219 -1.723030
Euro Gold -0.003753 -1.950192
Oil Euro -0.006973 -2.584827
Euro Oil -0.006324 -2.512779
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Error-Correction Model (ECM) for Testing for Long-Term and Short-Term Relationship
• The model is:
t
T
jjtjtj
T
iitititt XXdYYcZaX
11
1111
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Long term relationships
• Cannot reject a long term relationship between Oil and Gold
• Also, cannot reject a long term relationship between the Euro and Gold
• Finally, cannot reject a long term relationship between Oil and the Euro
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Results of Time Series Analysis
• Random Walks Confirmed
• Cointegration Confirmed
• Oil Prices are Driven by Gold and the Euro
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From Time Series to Neural Network
Dependent Variable Reg. Top 5 Variables NN Top 5 Variables
Euro
LEuroM1 LEuroM1
LGoldM1 LGoldM1
LGoldM2 LGoldM2
LEuroM3 LOilM1
LEuroM4 LOilM2
Oil
LOilM1 LOilM1
LEuroM5 LOilM2
LGoldM1 LGoldM1
LEuroM3 LGoldM2
LGoldM3 LEuroM5
Gold
LGoldM1 LGoldM1
LOilM1 LOilM1
LOilM2 LOilM2
LEuroM2 LGoldM2
LEuroM4 LEuroM4
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Conclusions
• From Old Independent Relationships
• To New Interrelated Relationships
• More work needed to study relationships during the financial crisis