1. 1 Takehome One 2008

2. 2 3 month treasury bill rate

3. 3 5 year Treasury

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6. 6 A measure of the term structure

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9. 9 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. Questions: Takehome One

10. 10 Histogram and Stats for Five Year

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12. 12 Unit Root test for GS5

13. 13 Histogram and Stats for Term

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16. 16Co-integration 1*TS5 – 1*TB3MS = Term 1*TS5 – 1*TB3MS = Term EvolutionaryStationary

17. 17 Modeling Term PACF ACF

18. 18Specification PACF(u) AR(p) PACF(u) AR(p) ACF(u) MA(q) ACF(u) MA(q)

19. 19 Best AR Model Ar(1) ar(2) ar(3) ser = 0.307 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) 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(5) ser = 0.3048 Ar(1) ar(2) ar(3) ar(4) ar(6) ser = 0.3045 Ar(1) ar(2) ar(3) ar(4) ar(6) ser = 0.3045

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22. 22 Specification Ar(1) ar(2) : look at residuals Ar(1) ar(2) : look at residuals Ar(1) ar(2) ar(3) : 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) : look at residuals Ar(1) ar(2) ar(3) ma(3) ma(9) : look at residuals Ar(1) ar(2) ar(3) ma(3) ma(9) : look at residuals ADD MA(15) ADD MA(15) ADD MA(20) ADD MA(20) ADD MA(21), ser = 0.295 ADD MA(21), ser = 0.295

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28. 28Validation Correlogram of residuals Correlogram of residuals Actual, fitted & residual graph Actual, fitted & residual graph Serial correlation test Serial correlation test Histogram of residuals Histogram of residuals

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32. 32 Within Sample Forecasting Re-estimate model from 1953:04 -2007:04 Re-estimate model from 1953:04 -2007:04

33. 33 In sample forecast: 2007:04-2008:04

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35. 35 Sample: 2005:01 – 2008:04 Quick menu: show

36. 36 In sample forecast

37. 37 Out of sample forecast Procs: expand 1953:04 – 2008:12 Procs: expand 1953:04 – 2008:12 Sample 1953:04 – 2008:12 Sample 1953:04 – 2008:12

38. 38 Out of Sample Forecast

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40. 40 Out of Sample Forecast

41. 41ARCH

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43. 43 ARCH: when Inverted Term Structure

44. 44 5 yr: 3.23 3 m: 1.86 Term; 1.37

45. 45 Estimate ARCH/GARCH

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47. 47Diagnostics Correlogram of standardized residuals Correlogram of standardized residuals Actual, fitted, residual graph Actual, fitted, residual graph correlogram of standardized residuals squared correlogram of standardized residuals squared LM ARCH test LM ARCH test

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49. 49 Arch LM Test

50. 50 Histogram of Standardized Residuals

51. 51 Estimate of Conditional Variance h

52. 52 Estimate of a Simpler Model with ARCH

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54. 54 Ordinary residuals from ARFOUR, ARCH

55. 55Appendix

56. 56 Alternative model #1

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60. 60 Residuals from model

61. 61 Alternative model #2

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65. 65 Autoregressive Conditional Heteroskedasticity

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