1 Takehome One 2008. 2 3 month treasury bill rate.

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Presentation transcript:

1 Takehome One 2008

2 3 month treasury bill rate

3 5 year Treasury

4

5

6 A measure of the term structure

7

8

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 Questions: Takehome One

10 Histogram and Stats for Five Year

11

12 Unit Root test for GS5

13 Histogram and Stats for Term

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15

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

17 Modeling Term PACF ACF

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

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

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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 = ADD MA(21), ser = 0.295

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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 Within Sample Forecasting Re-estimate model from 1953: :04 Re-estimate model from 1953: :04

33 In sample forecast: 2007: :04

34

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

36 In sample forecast

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 Out of Sample Forecast

39

40 Out of Sample Forecast

41ARCH

42

43 ARCH: when Inverted Term Structure

44 5 yr: m: 1.86 Term; 1.37

45 Estimate ARCH/GARCH

46

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

48

49 Arch LM Test

50 Histogram of Standardized Residuals

51 Estimate of Conditional Variance h

52 Estimate of a Simpler Model with ARCH

53

54 Ordinary residuals from ARFOUR, ARCH

55Appendix

56 Alternative model #1

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58

59

60 Residuals from model

61 Alternative model #2

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65 Autoregressive Conditional Heteroskedasticity

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