United States Imports

1
United States Imports

• Michael Williams
• Kevin Crider
• Andreas Lindal
• Jim Huang
• Juan Shan

2
Agenda
Introduction
Data
Modeling
Results
Conclusion
3
Introduction
Introduction
Data
Modeling
Results
Conclusion

• US is ranked as No. 4 globalized county in the
  world
• Import is a key index to measure globalization

Source ChristianSarkar.com
4
Introduction
Introduction
Data
Modeling
Results
Conclusion

• The ratio of US import good/service to GDP is
  increasing
• United States is transforming from a closed
  economy to an open environment

5
IMPORTS Trend
Introduction
Data
Modeling
Results
Conclusion
Billions of Dollars

• Trace shows increasing trend with time

Year
6
IMPORTS Histogram
Introduction
Data
Modeling
Results
Conclusion
7
IMPORTS Correlogram
Introduction
Data
Modeling
Results
Conclusion

• Big spike at lag one on PACF
• Suspicion of unit root

8
IMPORTS ADF Test
Introduction
Data
Modeling
Results
Conclusion

• Time series is not stationary
• Needs prewhitening before we could apply Box
  Jenkins modeling

9
DIMPORTS Histogram
Introduction
Data
Modeling
Results
Conclusion

• High Kurtosis discards normality
• More needs to be done to explain the trend

10
Dickey-Fuller Test
Introduction
Data
Modeling
Results
Conclusion

• Unit root test confirms stationarity
• Regression can now be performed

11
DIMPORTS Correlogram
Introduction
Data
Modeling
Results
Conclusion

• Spike at lag one and two in PACF
• Structure indicates a possible AR(2)

12
AR Model Estimation
Introduction
Data
Modeling
Results
Conclusion

• Both AR components are significant
• High F-stat

13
Correlogram of AR Model
Introduction
Data
Modeling
Results
Conclusion

• Correlogram looks orthogonal, but Q-stats are
  significant

14
ARCH Test Results
Introduction
Data
Modeling
Results
Conclusion

• ARCH test indicates that ARCH term is needed in
  the model to account for conditional variance

15
ARCH Model Estimation
Introduction
Data
Modeling
Results
Conclusion

• Both ARCH terms and GARCH term turn out
  significant

16
ARCH Model Correlogram
Introduction
Data
Modeling
Results
Conclusion

• Q-statistic stays inside confidence interval
• Correlogram is orthogonal

17
ARCH Residual Histogram
Introduction
Data
Modeling
Results
Conclusion
18
Actual, Fitted, Residuals
Introduction
Data
Modeling
Results
Conclusion

• Residuals graph indicates heteroskedasticity
• Likely would be improved with VAR Model

19
Validating ARCH model
Introduction
Data
Modeling
Results
Conclusion

• Forecast gives a good fit compared to the actual
  data

20
2008 Forecast
Introduction
Data
Modeling
Results
Conclusion
21
Conclusion

• Questions?

Introduction
Data
Modeling
Results
Conclusion

• US Imports should continue to grow faster than
  GDP
• Perhaps there are other techniques we could use
  in the future to address the correlation in our
  residuals