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Analysis of the Level and Variance of Gasoline Prices in the U.S. (1991-2014)

Analysis of the Level and Variance of Gasoline Prices in the U.S. (1991-2014). Lorenzo Borghi and Nathan Wiseman STAT 758 – Time Series Analysis Dr. Ilya Zaliapin. Outline. Goals Data Preprocessing Model Results Conclusion Limitations. goals.

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Analysis of the Level and Variance of Gasoline Prices in the U.S. (1991-2014)

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  1. Analysis of the Level and Variance of Gasoline Prices in the U.S. (1991-2014) Lorenzo Borghi and Nathan Wiseman STAT 758 – Time Series Analysis Dr. IlyaZaliapin

  2. Outline • Goals • Data • Preprocessing • Model • Results • Conclusion • Limitations

  3. goals • Find a transformation that makes the TS stationary • Estimate ARMA and GARCH Models • Provide dynamic forecasts that account for volatility clustering • Use the estimated conditional variances as a parameter in a model of vehicle choice and use in the future

  4. DATA

  5. Applying the Box-Jenkins Approach ACF - One first-difference ACF - Two first differences

  6. P values of the Box-LJUNG TEST Various orders of difference operators () log differenced series icorresponds to lags 1 to 53 j corresponds to the order of the operator (up to 10). The only operator that significantly improves the outcome of the test is the lag-2 operator

  7. weekly values of ()ln(Price)

  8. Grid search for arma order

  9. Assessing the ARMA (6, 6) Model Causality -Using thepolyroot command in R, it is found that the AR terms have a root of 0.41 Invertibility -The MA terms have a root of 0.06, which implies non-invertibility

  10. Best Fitting ARMA/GARCH Model

  11. Forecasts Accounting for Volatility Clustering

  12. Assessing Forecast Quality

  13. Conclusions • Adding the GARCH Model leads to a model that can account for how uncertain forecasting becomes in volatile periods • The overall forecasts have a significant positive correlation (r=0.789) with the observed values

  14. Limitations

  15. Questions?

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