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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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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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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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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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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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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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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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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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!