Transcript Application of ARIMA and GARCH Models to forecast the Gold

Application of ARIMA and GARCH Models
to forecast the Gold Futures Prices
Dr. Nupur Hetamsaria
(ICFAI Business School, Hyderabad)
&
Mithun Maity
(Karvy Comtrade, Hyderabad)
NICR Workshop, October 10th 2007
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Gold: An Investment Tool
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Equities and Commodities
Gold forms 45% of total futures trading globally
An effective hedging tool
Higher liquidity than other real assets
Oil price impact on Gold
Resale value of Gold
Forecasting the future Gold prices
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Data and Methodology
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Daily prices from NYMEX and COMEX
14 years, appx. 3500 data points
ARIMA
GARCH
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Price Graph of Gold Prices
800
700
600
500
400
300
200
500
1000
1500
2000
2500
GOLD
October 10th 2007
Nupur Hetamsaria & Mithun Maity
3000
Stationarity
ADF Test Statistic
0.313324 1% Critical Value*
-3.43532
PP Test Statistic
0.439737 1% Critical Value*
-3.4353
•Gold Price series is not stationary.
•First Difference of the price series.
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Intercept
Trend
and
Intercept
Dickey Fuller Test
Philip Peron Test
ADF Test
Statistic
PP Test
Statistic
ADF Test
Statistic
ADF Test
Statistic
-23.863
-23.9215
-23.8299
None
October 10th 2007
1% Critical Value*
-3.4353
Akaike info criterion
Schwarz criterion
1% Critical Value*
-3.4353
5.482112
Akaike info criterion
5.485396
5.492703
Schwarz criterion
5.488923
1% Critical Value*
-3.9662
PP Test
Statistic
-60.86858
1% Critical Value*
-3.9662
Akaike info criterion
5.481955
Akaike info criterion
5.485005
Schwarz criterion
5.494311
Schwarz criterion
5.490296
1% Critical Value*
-2.5664
1% Critical Value*
-2.5664
Akaike info criterion
5.481968
Akaike info criterion
5.485379
Schwarz criterion
5.490794
Schwarz criterion
5.487142
PP Test
Statistic
-60.9116
-60.84753
Nupur Hetamsaria & Mithun Maity
40
20
0
-20
-40
-60
500
1000
1500
2000
2500
DGOLD
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Nupur Hetamsaria & Mithun Maity
3000
Normality
Mean
0.086144
Median
0
Skewness
-0.74033
Kurtosis
18.11785
Jarque Barra
33582.55
Probability
0
Kurtosis high, indicating a ‘fat tail’ distribution or a leptokurtic
distribution.
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Correlogram
Variable
Coefficient
Std. Error
t-Statistic
Prob.
AR(1)
0.621301
0.056157
11.06371
0
AR(3)
-0.134398
0.032265
-4.165387
0
AR(6)
0.207676
0.061152
3.396052
0.0007
AR(11)
0.397422
0.049314
8.058982
0
AR(17)
-0.116156
0.055514
-2.09239
0.0365
AR(21)
-0.249367
0.024521
-10.16953
0
AR(28)
-0.050772
0.015572
-3.260515
0.0011
MA(1)
-0.641257
0.05479
-11.70385
0
MA(3)
0.174463
0.03261
5.350072
0
MA(6)
-0.245322
0.056933
-4.308968
0
MA(11)
-0.435156
0.046657
-9.326747
0
MA(17)
0.171075
0.058323
2.933233
0.0034
MA(21)
0.236852
0.023383
10.12933
0
October 10th 2007
Nupur Hetamsaria & Mithun Maity
0.10
0.05
0.00
0.10
-0.05
0.05
-0.10
0.00
-0.05
-0.10
500
1000
1500
Residual
October 10th 2007
2000
2500
Actual
Nupur Hetamsaria & Mithun Maity
3000
Fitted
Heteroscedasticity
ARCH Test:
F-statistic
74.38698
Probability
0
Obs*R-squared
72.86433
Probability
0
October 10th 2007
Nupur Hetamsaria & Mithun Maity
GARCH: Mean equation
GARCH(1,1)
Mean Equation
Coefficient
Std. Error
z-Statistic
Prob.
AR(6)
-0.03903
0.018965
-2.05778
0.0396
AR(12)
-0.04492
0.018417
-2.43881
0.0147
AR(45)
-0.04522
0.017644
-2.56266
0.0104
AR(79)
0.049338
0.01843
2.677098
0.0074
AR(89)
-0.03371
0.017259
-1.95314
0.0508
October 10th 2007
Nupur Hetamsaria & Mithun Maity
GARCH (1,1)
Variance Equation
C
9.54E-08
9.48E-08
1.00621
0.3143
ARCH(1)
0.04162
0.01339
3.10826
0.0019
GARCH(1)
0.960488
0.012698
75.64137
0
October 10th 2007
Nupur Hetamsaria & Mithun Maity
ARCH Test:
F-statistic
1.513348
Probability
0.218712
Obs*R-squared
1.513561
Probability
0.218597
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Performance of In sample forecast
Root Mean Squared Error
7.622201
Theil Inequality Coefficient
0.006179
Bias proportion
0.000069
Variance proportion
0.000121
covariance proportion
0.99981
October 10th 2007
Nupur Hetamsaria & Mithun Maity
Performance of out of sample forecast
660
640
620
600
580
560
3400 3410 3420 3430 3440 3450 3460 3470 3480 3490
GOLD
October 10th 2007
GOLDFS
Nupur Hetamsaria & Mithun Maity