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F- Test Applications. Time Series Applications. Chow Test for structural change. Actual, Fitted, Residual graph. The Gann Initiative. 1977-Limit Government in Real Terms Per Capita Two periods 1968-69 through 1977-78 1978-79 through 2007-08. Genr periodone=0, type in ones

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Time series applications
Time Series Applications

  • Chow Test for structural change



The gann initiative
The Gann Initiative

  • 1977-Limit Government in Real Terms Per Capita

  • Two periods

    • 1968-69 through 1977-78

    • 1978-79 through 2007-08


Genr periodone=0, type in ones

Genr periodtwo=1, type in zeros


Genr timeone=periodone*time

Genr timetwo=periodtwo*time


Regression
Regression

  • Ratio = c(1)*periodone + c(2)*timeone + c(3)*periodtwo + c(4)*timetwo +e(t)


F test
F-Test

  • F2, 36 = [SSR2 - SSR4 ]/2 ÷ SSR4/(40-4)

  • F2, 36 = [13.31 – 7.40]/2 ÷ 7.40/36

  • F2, 36 = 2.96/0.206 = 14.4




Can you go from 2 parameters to 4 parameters
Can you go from 2 parameters to 4 parameters?

  • Yes, there is a significant increase in explained variance, indicating a structural change after the passage of the Gann Initiative in 1977


Alternatively can you estimate a single time trend instead of two time trends
Alternatively, can you estimate a single time trend instead of two time trends?

  • No, two time trends fits the data significantly better


Wald test
Wald Test of two time trends?


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