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Takehome One

Takehome One. 2008. 3 month treasury bill rate. 5 year Treasury. A measure of the term structure. Questions: Takehome One.

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Takehome One

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  1. Takehome One 2008

  2. 3 month treasury bill rate

  3. 5 year Treasury

  4. A measure of the term structure

  5. Questions: Takehome One 1. You should try this so that you know at least one way of obtaining time series from FRED. If you have difficulty, an Excel file called Takeone, is available on the class page. 2. Generate a time series called term that is the difference between GS5 and TB3MS. 3. Is term stationary, i.e. are GS5 and TB3ms co-integrated? 4. Is term normally distributed? 5. Estimate your best autoregressive model for term. 6. Estimate your best ARMA model for term through April 2007 and see how well a forecast for this model fits the next 12 months. 7. Re-estimate your best model for term through April 2008 and forecast for the remaining months of 2008.

  6. Histogram and Stats for Five Year

  7. Unit Root test for GS5

  8. Histogram and Stats for Term

  9. Co-integration • 1*TS5 – 1*TB3MS = Term Evolutionary Stationary

  10. Modeling Term ACF PACF

  11. Specification • PACF(u) AR(p) • ACF(u) MA(q)

  12. Best AR Model • Ar(1) ar(2) ar(3) ser = 0.307 • Ar(1) ar(2) ar(3) ar(4) ser = 0.305 • Ar(1) ar(2) ar(3) ar(4) ar(5) ser = 0.3048 • Ar(1) ar(2) ar(3) ar(4) ar(6) ser = 0.3045

  13. Specification • Ar(1) ar(2) : look at residuals • Ar(1) ar(2) ar(3) : look at residuals • Ar(1) ar(2) ar(3) ma(3) : look at residuals • Ar(1) ar(2) ar(3) ma(3) ma(9) : look at residuals • ADD MA(15) • ADD MA(20) • ADD MA(21), ser = 0.295

  14. Validation • Correlogram of residuals • Actual, fitted & residual graph • Serial correlation test • Histogram of residuals

  15. Within Sample Forecasting • Re-estimate model from 1953:04 -2007:04

  16. In sample forecast: 2007:04-2008:04

  17. Sample: 2005:01 – 2008:04 Quick menu: show

  18. In sample forecast

  19. Out of sample forecast • Procs: expand 1953:04 – 2008:12 • Sample 1953:04 – 2008:12

  20. Out of Sample Forecast

  21. Out of Sample Forecast

  22. ARCH

  23. ARCH: when Inverted Term Structure

  24. 5 yr: 3.23 3 m: 1.86 Term; 1.37

  25. Estimate ARCH/GARCH

  26. Diagnostics • Correlogram of standardized residuals • Actual, fitted, residual graph • correlogram of standardized residuals squared • LM ARCH test

  27. Arch LM Test

  28. Histogram of Standardized Residuals

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