price of gold and us dollar index dwarakamayi polakam jennifer griffeth ashley arlotti rui feng ying...
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Price of Gold and US Dollar Index
Dwarakamayi PolakamJennifer GriffethAshley ArlottiRui FengYing FanQi HeQi Li
Group C Presentation
Overview
1
US Dollar Index
1.1 Analysis of DOLLARINDEX
1.2 Analysis of DLNDOLLAR
1.3 AR Model
1.4 Forecasting
3
Relationship Between Gold and US Dollar3.1 The Cross Correlogram3.2 Analysis of w and resm(Distributed Lag Model)3.3 Analysis of DLNGOLD and DLNDOLLAR3.4 Causality Test3.5 VAR Analysis
2
Price of Gold
2.1 Analysis of GOLD
2.2 Analysis of DLNGOLD
2.3 AR Model
2.4 GARCH Model
2.5 Forecasting
Part 1: US Dollar IndexThe First Model: DLNDOLLAR
1.1 Analysis of DOLLARINDEX• (1) Trace
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1975 1980 1985 1990 1995 2000 2005 2010
DOLLARINDEX
1.1 Analysis of DOLLARINDEX• (2) Histogram
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Series: DOLLARINDEXSample 1973M01 2011M12Observations 460
Mean 96.38014Median 95.11450Maximum 143.9059Minimum 69.74840Std. Dev. 13.92285Skewness 0.717355Kurtosis 3.745509
Jarque-Bera 50.10502Probability 0.000000
1.1 Analysis of DOLLARINDEX• (3) Correlogram
1.1 Analysis of DOLLARINDEX• (4) Unit Root Test
1.2 Analysis of DLNDOLLAR• (1) Trace
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DLNDOLLAR
1.2 Analysis of DLNDOLLAR• (2) Histogram
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-0.04 -0.02 0.00 0.02 0.04 0.06
Series: DLNDOLLARSample 1973M01 2011M12Observations 459
Mean -0.000956Median 7.48e-06Maximum 0.064728Minimum -0.053901Std. Dev. 0.017443Skewness -0.045088Kurtosis 3.335338
Jarque-Bera 2.306159Probability 0.315663
1.2 Analysis of DLNDOLLAR• (3) Correlogram
1.2 Analysis of DLNDOLLAR• (4) Unit Root Test
1.3 AR(1), AR(2) Model• (1) Add AR(1) and AR(2)
1.3 AR(1), AR(2) Model• (2a) Diagnostic - Actual, fitted and residual
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1975 1980 1985 1990 1995 2000 2005 2010
Residual Actual Fitted
1.3 AR(1), AR(2) Model• (2b) Diagnostic - Correlogram of residuals
1.3 AR(1), AR(2) Model• (2c) Diagnostic - Histogram of residuals
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-0.06 -0.04 -0.02 0.00 0.02 0.04 0.06
Series: ResidualsSample 1973M04 2011M04Observations 457
Mean -0.000583Median -0.000324Maximum 0.061955Minimum -0.058489Std. Dev. 0.016293Skewness 0.027234Kurtosis 3.982186
Jarque-Bera 18.42577Probability 0.000100
1.3 AR(1), AR(2) Model• (2d) Diagnostic - Serial Correlation test on residuals
1.3 AR(1), AR(2) Model• (2e) Diagnostic - Correlogram of residual squared
1.3 AR(1), AR(2) Model• (2f) Diagnostic - Heteroskedasticity test
1.4 Forecasting• (1) Confidence Interval of Two Standard Error
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M5 M6 M7 M8 M9 M10 M11 M12
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F_DLNDOLLAR ± 2 S.E.
1.4 Forecasting• (2) Forecast for Next Eight Months
Part 2: Price of GoldThe Second Model: DLNGOLD
2.1 Analysis of GOLD• (1) Trace
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1975 1980 1985 1990 1995 2000 2005 2010
Gold
2.1 Analysis of GOLD• (2) Histogram
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Series: GOLDSample 1973M01 2011M12Observations 460
Mean 412.1254Median 369.8350Maximum 1473.640Minimum 65.14000Std. Dev. 244.0885Skewness 1.963053Kurtosis 7.474542
Jarque-Bera 679.1870Probability 0.000000
2.1 Analysis of GOLD• (3) Correlogram
2.1 Analysis of GOLD• (4) Unit Root Test
2.2 Analysis of DLNGOLD• (1) Trace
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DLNGOLD
2.2 Analysis of DLNGOLD• (2) Histogram
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Series: DLNGOLDSample 1973M01 2011M12Observations 459
Mean 0.006795Median 0.000391Maximum 0.396786Minimum -0.187689Std. Dev. 0.051372Skewness 1.284874Kurtosis 11.27561
Jarque-Bera 1436.082Probability 0.000000
2.2 Analysis of DLNGOLD• (3) Correlogram
2.2 Analysis of DLNGOLD• (4) Unit Root Test
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (1) AIC, SIC, etc for Different Models
AIC SIC HQC DW AC PC
Serial Correlation
AR(1) AR(2) AR(11) -3.257 -3.23 -3.245 2.00007 7,8,21 7,8,14 no
AR(1) AR(2) AR(7) AR(8) AR(11) AR(18) -3.309 -3.254 -3.287 1.9924 19 5 no
AR(1) AR(2) AR(7) AR(8) AR(11) AR(18) AR(19) -3.3114 -3.2464 -3.2858 1.978217 - - no
AR(1) AR(2) AR(11) MA(7) MA(8) MA(11) -3.228 -3.183 -3.21 2.000898 29,35 35 yesAR(1) AR(2) AR(11) MA(7) MA(8) MA(11) MA(29) M,A(35) -3.234 -3.17114
-3.20945 1.989275 - - no
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (2) Add AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18)
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3a) Diagnostic - Actual, fitted and residual
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1975 1980 1985 1990 1995 2000 2005 2010
Residual Actual Fitted
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3b) Diagnostic - Correlogram of residuals
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3c) Diagnostic - Histogram of residuals
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Series: ResidualsSample 1974M08 2011M04Observations 441
Mean 0.003663Median 0.000718Maximum 0.342418Minimum -0.157438Std. Dev. 0.045535Skewness 1.051098Kurtosis 10.98224
Jarque-Bera 1251.988Probability 0.000000
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3d) Diagnostic - Serial Correlation test on residuals
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3e) Diagnostic - Correlogram of residual squared
2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3f) Diagnostic - Heteroskedasticity test
2.4 GARCH Model• (1) Add GARCH
2.4 GARCH Model• (2a) Diagnostic - Correlogram of residuals
2.4 GARCH Model• (2b) Diagnostic - Histogram of residuals
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Series: Standardized ResidualsSample 1974M08 2011M04Observations 441
Mean 0.080132Median 0.015133Maximum 5.214272Minimum -3.063264Std. Dev. 0.998728Skewness 0.539564Kurtosis 5.270940
Jarque-Bera 116.1610Probability 0.000000
2.4 GARCH Model• (2c) Diagnostic - Correlogram of residual squared
2.4 GARCH Model• (2d) Diagnostic - Heteroskedasticity test
2.5 Forecasting• (1) Confidence Interval of Two Standard Error
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F_DLNGOLD ± 2 S.E.
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2011
Forecast of Variance
2.5 Forecasting• (2) Forecast for Next Eight Months
Part 3: Relationship Between Gold and US Dollar
3.1 The Cross Section Correlogram
3.2 Analysis of w and resm• (1) Theoretical Analysis
LNGOLD(t)
= h0LNDOLLAR(t) + h1LNDOLLAR(t-1) + h2LNDOLLAR(t-2) +…+ e(t)
= (h0 + h1Z + h2Z2 +…) LNDOLLAR(t) + e(t) = h(z)LNDOLLAR(t) + e(t)
First Difference:
DLNGOLD(t) = h(z) DLNDOLLAR(t) + e(t)
Fit AR(2) model to DLNDOLLAR, B(z)*DLNDOLLAR = WN(t),
B(z)* DLNGOLD(t) = h(z)* B(z)*DLNDOLLAR(t) + B(z)* e(t)
W(t) = h(z) * resm + error(t)
3.2 Analysis of w and resm• (2a) Analysis of w and resm
3.2 Analysis of w and resm• (2b) Analysis of w and resm with AR terms
3.2 Analysis of w and resm• (3a) Diagnostic - Actual, fitted and residual
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3.2 Analysis of w and resm• (3b) Diagnostic - Correlogram of residuals
3.2 Analysis of w and resm• (3c) Diagnostic - Serial Correlation test on residuals
3.2 Analysis of w and resm• (3d) Diagnostic - Heteroskedasticity test
3.3 Analysis of DLNGOLD and DLNDOLLAR• (1) Analysis of DLNGOLD and DLNDOLLAR
3.3 Analysis of DLNGOLD and DLNDOLLAR• (2a) Diagnostic - Actual, fitted and residual
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3.3 Analysis of DLNGOLD and DLNDOLLAR• (2b) Diagnostic - Correlogram of residuals
3.3 Analysis of DLNGOLD and DLNDOLLAR• (2c) Diagnostic - Serial Correlation test on residuals
3.3 Analysis of DLNGOLD and DLNDOLLAR• (2d) Diagnostic - Heteroskedasticity test
3.4 Causality Test
Pairwise Granger Causality Tests
Date: 05/31/11 Time: 08:00
Sample: 1973:01 2011:12
Lags: 25
Null Hypothesis: Obs F-Statistic Probability
DLNDOLLARINDEX does not Granger Cause DLNGOLD 434 0.91269 0.58797
DLNGOLD does not Granger Cause DLNDOLLARINDEX 1.55018 0.04616
3.5 VAR Analysis• (1a) VAR Analysis
DLNGOLD DLNDOLLARINDEX
DLNGOLD(-1) 0.185969 0.008348 (0.05448) (0.01922) (3.41364) (0.43432)
DLNGOLD(-2) -0.150826 0.025431 (0.05538) (0.01954) (-2.72354) (1.30163)
DLNGOLD(-7) 0.112218 0.006677 (0.05538) (0.01954) (2.02625) (0.34176)
DLNGOLD(-11) 0.139112 -0.022972 (0.05538) (0.01954) (2.51182) (-1.17571)
DLNGOLD(-18) -0.111669 0.000383 (0.05360) (0.01891) (-2.08344) (0.02024)
DLNGOLD(-19) -0.046602 0.043418 (0.05325) (0.01879) (-0.87519) (2.31119)
DLNDOLLARINDEX(-1) -0.156528 0.376342 (0.15434) (0.05445) (-1.01416) (6.91147)
DLNDOLLARINDEX(-18) -0.159882 0.120925 (0.16132) (0.05691) (-0.99108) (2.12471)
3.5 VAR Analysis• (1a) Impulse Analysis
3.5 VAR Analysis• (1b) VAR Analysis
Conclusion
1. Dlndollarindex - AR model final model to forecast.
2. Dlngold- GARCH(1,1) Final model to forecast.
3. Dollar weakens Gold price increases.
4. One way causality, Gold to Dollar Index.
5. Gold price and Dollar Index inversely correlated.
Thank you!
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