F Test Applications 1 Time Series Applications Chow Test for structural change 2 3 4 5 Actual Fitted Residual graph 8 7 1 5 6 1 0 5 0 5 4 0 0 0 5 1 0 70 75 80 Residual 85 90 Actual 95 00 05 Fitted 6 The Gann Initiative 1977 Limit Government in Real Terms Per Capita Two periods 1968 69 through 1977 78 1978 79 through 2007 08 7 Genr periodone 0 type in ones Genr periodtwo 1 type in zeros 8 Genr timeone periodone time Genr timetwo periodtwo time 9 10 Regression Ratio c 1 periodone c 2 timeone c 3 periodtwo c 4 timetwo e t 11 12 8 7 6 1 0 5 0 5 4 0 0 0 5 1 0 1 5 70 75 80 Residual 85 90 Actual 95 00 05 Fitted 13 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 14 Genr Fvar rfdist 2 36 Genr Density dfdist Fvar 2 36 15 F density for 2 and 36 Degrees of Freedom F density for 2 and 36 degrees of freedom 1 0 14 4 DENSITY 0 8 0 6 3 27 0 4 0 2 5 0 0 0 2 4 6 FVAR 8 10 16 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 17 Alternatively can you estimate a single time trend instead of two time trends No two time trends fits the data significantly better 18 19 Wald Test 20 21 22 23 24
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