Download - Price of Gold and US Dollar Index
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Price of Gold and US Dollar Index
Dwarakamayi PolakamJennifer GriffethAshley ArlottiRui FengYing FanQi HeQi Li
Group C Presentation
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Overview
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US Dollar Index
1.1 Analysis of DOLLARINDEX
1.2 Analysis of DLNDOLLAR
1.3 AR Model
1.4 Forecasting
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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
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Price of Gold
2.1 Analysis of GOLD
2.2 Analysis of DLNGOLD
2.3 AR Model
2.4 GARCH Model
2.5 Forecasting
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Part 1: US Dollar IndexThe First Model: DLNDOLLAR
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1.1 Analysis of DOLLARINDEX• (1) Trace
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DOLLARINDEX
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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
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1.1 Analysis of DOLLARINDEX• (3) Correlogram
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1.1 Analysis of DOLLARINDEX• (4) Unit Root Test
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1.2 Analysis of DLNDOLLAR• (1) Trace
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DLNDOLLAR
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1.2 Analysis of DLNDOLLAR• (2) Histogram
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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
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1.2 Analysis of DLNDOLLAR• (3) Correlogram
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1.2 Analysis of DLNDOLLAR• (4) Unit Root Test
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1.3 AR(1), AR(2) Model• (1) Add AR(1) and AR(2)
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1.3 AR(1), AR(2) Model• (2a) Diagnostic - Actual, fitted and residual
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Residual Actual Fitted
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1.3 AR(1), AR(2) Model• (2b) Diagnostic - Correlogram of residuals
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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
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1.3 AR(1), AR(2) Model• (2d) Diagnostic - Serial Correlation test on residuals
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1.3 AR(1), AR(2) Model• (2e) Diagnostic - Correlogram of residual squared
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1.3 AR(1), AR(2) Model• (2f) Diagnostic - Heteroskedasticity test
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1.4 Forecasting• (1) Confidence Interval of Two Standard Error
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M5 M6 M7 M8 M9 M10 M11 M12
2011
F_DLNDOLLAR ± 2 S.E.
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1.4 Forecasting• (2) Forecast for Next Eight Months
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Part 2: Price of GoldThe Second Model: DLNGOLD
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2.1 Analysis of GOLD• (1) Trace
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Gold
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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
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2.1 Analysis of GOLD• (3) Correlogram
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2.1 Analysis of GOLD• (4) Unit Root Test
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2.2 Analysis of DLNGOLD• (1) Trace
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DLNGOLD
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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
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2.2 Analysis of DLNGOLD• (3) Correlogram
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2.2 Analysis of DLNGOLD• (4) Unit Root Test
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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 noAR(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
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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)
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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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Residual Actual Fitted
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2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3b) Diagnostic - Correlogram of residuals
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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
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2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3d) Diagnostic - Serial Correlation test on residuals
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2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3e) Diagnostic - Correlogram of residual squared
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2.3 AR(1) , AR(2), AR(7), AR(8), AR(11) and AR(18) Model• (3f) Diagnostic - Heteroskedasticity test
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2.4 GARCH Model• (1) Add GARCH
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2.4 GARCH Model• (2a) Diagnostic - Correlogram of residuals
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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
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2.4 GARCH Model• (2c) Diagnostic - Correlogram of residual squared
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2.4 GARCH Model• (2d) Diagnostic - Heteroskedasticity test
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2.5 Forecasting• (1) Confidence Interval of Two Standard Error
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M5 M6 M7 M8 M9 M10 M11 M122011
F_DLNGOLD ± 2 S.E.
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.00112
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M5 M6 M7 M8 M9 M10 M11 M122011
Forecast of Variance
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2.5 Forecasting• (2) Forecast for Next Eight Months
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Part 3: Relationship Between Gold and US Dollar
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3.1 The Cross Section Correlogram
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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)
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3.2 Analysis of w and resm• (2a) Analysis of w and resm
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3.2 Analysis of w and resm• (2b) Analysis of w and resm with AR terms
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3.2 Analysis of w and resm• (3a) Diagnostic - Actual, fitted and residual
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Residual Actual Fitted
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3.2 Analysis of w and resm• (3b) Diagnostic - Correlogram of residuals
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3.2 Analysis of w and resm• (3c) Diagnostic - Serial Correlation test on residuals
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3.2 Analysis of w and resm• (3d) Diagnostic - Heteroskedasticity test
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3.3 Analysis of DLNGOLD and DLNDOLLAR• (1) Analysis of DLNGOLD and DLNDOLLAR
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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
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3.3 Analysis of DLNGOLD and DLNDOLLAR• (2c) Diagnostic - Serial Correlation test on residuals
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3.3 Analysis of DLNGOLD and DLNDOLLAR• (2d) Diagnostic - Heteroskedasticity test
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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
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3.5 VAR Analysis• (1a) VAR Analysis
DLNGOLD DLNDOLLARINDEXDLNGOLD(-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)
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3.5 VAR Analysis• (1a) Impulse Analysis
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3.5 VAR Analysis• (1b) VAR Analysis
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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.
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Thank you!