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F- Test Applications

This study utilizes the Chow test to identify structural changes in time series data, focusing on changes associated with the Gann Initiative of 1977. By comparing two distinct periods (1968-79 and 1978-08), we analyze regression outcomes using F-tests to evaluate the explained variance. The results demonstrate a significant increase in explained variance after the Gann Initiative, indicating a structural change. Further, we explore the adequacy of two time trends as opposed to a single trend, confirming that multiple trends provide a significantly better fit for the data.

jamal-hines
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F- Test Applications

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  1. F- Test Applications

  2. Time Series Applications • Chow Test for structural change

  3. Actual, Fitted, Residual graph

  4. The Gann Initiative • 1977-Limit Government in Real Terms Per Capita • Two periods • 1968-69 through 1977-78 • 1978-79 through 2007-08

  5. Genr periodone=0, type in ones Genr periodtwo=1, type in zeros

  6. Genr timeone=periodone*time Genr timetwo=periodtwo*time

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

  8. 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

  9. Genr: Fvar=@rfdist(2, 36) Genr: Density=@dfdist(Fvar, 2, 36)

  10. F density for 2 and 36 Degrees of Freedom 14.4 3.27 5%

  11. 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

  12. Alternatively, can you estimate a single time trend instead of two time trends? • No, two time trends fits the data significantly better

  13. Wald Test

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