F-statistic in an AR(1)

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bparksb
Posts: 56
Joined: Mon Mar 21, 2011 9:26 pm

F-statistic in an AR(1)

Postby bparksb » Sun Sep 22, 2013 4:02 pm

Why doesn't the reported F-statistic in an AR(1) regression agree with any Wald test of the coefficients.
The following code produces the table (how do you get monospaced so you can do a table formatted?)
F P
F-stat from regression 11.79593 1.74E-08
C(2)=C(3)=C(4)=C(5)=C(6)=C(7)=0 5.984429 0.0001
C(2)=C(3)=C(4)=C(5)=C(6)=C(7)=C(8)=0 7.967920 0.0000
C(1)=C(2)=C(3)=C(4)=C(5)=C(6)=C(7)=0 138.7015 0.0000
C(1)=C(2)=C(3)=C(4)=C(5)=C(6)=C(7)=C(8)=0 123.1954 0.0000
R^2/(1-R^2)*(N-K-1)/#res 11.79593

The F-Statistic is R^2/(1-R^2)*DOF/#restrictions but it does not agree with the Wald test. For a regression without the AR(1) coefficient, the Wald test and the F-Statistic and the R^2 calculations agree.
Code to create the table, R^2 calculation is hand entered.

Code: Select all

wfcreate(wf=test_ar_F) a 1950 2004 series STDEVWP series FRAGENTS series DRAFT series EXPAN series GAMES series POPPCT series TEAMS STDEVWP.fill 0.1027475073933601,0.09058467000000001,0.1029122620820999,0.1089010089635849,0.1201975420117378,0.09141733000000001,0.09009623999999999,0.08241672999999999,0.05193774402141571,0.05761597,0.08324903,0.09662496,0.09573725,0.08316496,0.08339663,0.08801164,0.06376486000000001,0.06533477,0.06001708,0.09245352,0.07788844,0.07242656499147415,0.07337721,0.06394867599010468,0.06170581,0.07206608000000001,0.07307347,0.088834,0.0750376,0.08099268,0.07104561,0.07839835000000001,0.06462069,0.06052007,0.05518005415797234,0.07779896,0.06329833,0.06057028,0.07422470000000001,0.06093438,0.05586484,0.05970393493771553,0.06323637,0.07499280999999999,0.06827225536108017,0.0708773,0.06186301,0.05921086,0.08332833000000001,0.07628321,0.06166595,0.08049928000000001,0.09147087,0.08260375,0.08328445 FRAGENTS.fill 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,2,22,22,38,43,48,42,41,45,55,61,79,76,73,91,115,99,151,97,131,137,116,139,138,117,135,155,156,211 DRAFT.fill 0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1 EXPAN.fill 0,0,0,0,0,0,0,0,0,0,0,1,1,0,0,0,0,0,0,1,0,0,0,0,0,0,0,1,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,1,0,0,0,0,1,0,0,0,0,0,0 GAMES.fill 154.8,154.9,154.9,155,154.6,154.3,154.9,154.4,154.4,154.8,154.5,158.9,162.1,161.9,162.6,162.3,161.5,162,162.5,162.2,162,161.5,154.9,161.9,162.1,161.2,161.6,161.8,161.7,161.5,161.9,107.2,162.1,162.2,161.9,161.8,161.8,161.9,161.5,162,161.9,161.8,162,162.1,114.2,144,162.1,161.8,162.1,161.8,161.9,161.9,161.7,161.9,161.9 POPPCT.fill 0.0002626888162922114,0.000258267973549664,0.0002538832486607134,0.0002497125242371112,0.0002453598426654935,0.0002410637680441141,0.0002368222776567563,0.0002325796,0.000228725781198591,0.0002249344,0.0002213967,0.0002449759631417692,0.0002680423,0.0002642122562974691,0.0002605675836093724,0.0002573301,0.0002543748,0.0002516203676350415,0.0002491205523256213,0.0002960376,0.0002926084562204778,0.0002889329,0.0002858558,0.0002831407,0.0002805653493851423,0.0002778122434392571,0.0002751849824562669,0.0002951333590317518,0.0002920238766819239,0.0002888176531996578,0.0002860604727175087,0.0002832667,0.0002805782,0.0002780249,0.0002756282337941229,0.0002731967251747847,0.0002706834638956934,0.0002682747435756028,0.0002658497833181173,0.0002633506373967975,0.0002605582,0.0002577799,0.0002548722841311246,0.0002715466252993792,0.0002688925596885383,0.0002663589257281274,0.0002639233,0.0002614051,0.0002775228640530258,0.0002750367566477507,0.0002657899167388678,0.0002630713,0.0002604402543511242,0.0002579005376901478,0.0002542166621424258 TEAMS.fill 16,16,16,16,16,16,16,16,16,16,16,18,20,20,20,20,20,20,20,24,24,24,24,24,24,24,24,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,26,28,28,28,28,28,30,30,30,30,30,30,30 param c(1) 0 c(2) 0 c(3) 0 c(4) 0 c(5) 0 c(6) 0 c(7) 0 c(8) 0 equation eq01.LS(S=0,Z,+SHOWOPTS) STDEVWP C FRAGENTS DRAFT EXPAN GAMES POPPCT TEAMS AR(1) 'equation eq01.LS(S=0,Z,+SHOWOPTS) STDEVWP C FRAGENTS AR(1) !i=1 table(7,3) Fstat_Wald Fstat_Wald(1,2)="F" Fstat_Wald(1,3)="P" !j=!i+1 Fstat_Wald(!i,1)="F-stat from regression" matrix (5,2) waldtests waldtests(!i,1) = eq01.@f waldtests(!i,2) = eq01.@fprob Fstat_Wald(!i+1,2)=eq01.@f Fstat_Wald(!i+1,3)=eq01.@fprob freeze(waldtable) eq01.wald c(2)=c(3)=c(4)=c(5)=c(6)=c(7)=0 !i=!i+1 waldtests(!i,1)=@val(waldtable(6,2)) waldtests(!i,2)=@val(waldtable(6,4)) Fstat_Wald(!i+1,1)=@wdrop(waldtable(10,1),"Null Hypothesis: ") Fstat_Wald(!i+1,2)=waldtable(6,2) Fstat_Wald(!i+1,3)=waldtable(6,4) d waldtable freeze(waldtable) eq01.wald c(2)=c(3)=c(4)=c(5)=c(6)=c(7)=c(8)=0 !i=!i+1 waldtests(!i,1)=@val(waldtable(6,2)) waldtests(!i,2)=@val(waldtable(6,4)) Fstat_Wald(!i+1,1)=@wdrop(waldtable(10,1),"Null Hypothesis: ") Fstat_Wald(!i+1,2)=waldtable(6,2) Fstat_Wald(!i+1,3)=waldtable(6,4) d waldtable freeze(waldtable) eq01.wald c(1)=c(2)=c(3)=c(4)=c(5)=c(6)=c(7)=0 !i=!i+1 waldtests(!i,1)=@val(waldtable(6,2)) waldtests(!i,2)=@val(waldtable(6,4)) Fstat_Wald(!i+1,1)=@wdrop(waldtable(10,1),"Null Hypothesis: ") Fstat_Wald(!i+1,2)=waldtable(6,2) Fstat_Wald(!i+1,3)=waldtable(6,4) d waldtable freeze(waldtable) eq01.wald c(1)=c(2)=c(3)=c(4)=c(5)=c(6)=c(7)=c(8)=0 !i=!i+1 waldtests(!i,1)=@val(waldtable(6,2)) waldtests(!i,2)=@val(waldtable(6,4)) Fstat_Wald(!i+1,1)=@wdrop(waldtable(10,1),"Null Hypothesis: ")+@trim(waldtable(11,1)) Fstat_Wald(!i+1,2)=waldtable(6,2) Fstat_Wald(!i+1,3)=waldtable(6,4) d waldtable !i=!i+1 Fstat_Wald(!i+1,1)="R^2/(1-R^2)*(N-K-1)/#res" scalar Rsq=eq01.@r2 Fstat_Wald(!i+1,2)=Rsq/(1-Rsq)*(54-8)/7 Fstat_Wald(!i+1,3)=Rsq show Fstat_Wald
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bparksb
Posts: 56
Joined: Mon Mar 21, 2011 9:26 pm

Re: F-statistic in an AR(1)

Postby bparksb » Sun Sep 22, 2013 4:08 pm

Sorry, Eviews 8 SEP 20 2013
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EViews Gareth
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Re: F-statistic in an AR(1)

Postby EViews Gareth » Sun Sep 22, 2013 9:40 pm

The f-statistic is calculated as, as you point out, R^2/(1-R^2)*DOF. In a simple OLS with constant, this is equal to the Wald test version. In non-simple OLS cases it often does not. EViews always reports the R^2 based calculation, even if you're not performing simple OLS.

If you want the Wald test version all the time, the best thing to do is to perform the Wald test.


Note that a similar argument could be made for cases where you have robust standard errors. For years EViews only reported the R^2 based version there too, which, obviously, was also not equal to the Wald test. In EViews 8 we now also report the Wald version for cases with robust standard errors.
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bparksb
Posts: 56
Joined: Mon Mar 21, 2011 9:26 pm

Re: F-statistic in an AR(1)

Postby bparksb » Mon Sep 23, 2013 4:56 am

Not exactly what the manual states around 24.17
... the reported F-statistic (which Eviews always computes as W/q), ...
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EViews Gareth
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Re: F-statistic in an AR(1)

Postby EViews Gareth » Mon Sep 23, 2013 8:07 am

That section is talking about the Wald test. Not the F-statistic reported on the equation output (which I presume is the one you were originally talking about?). The manual states that the F-statistic shown on the equation output is calculated as:
R^2/(k-1) / (1-R^2)/(T-k)
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bparksb
Posts: 56
Joined: Mon Mar 21, 2011 9:26 pm

Re: F-statistic in an AR(1)

Postby bparksb » Mon Sep 23, 2013 3:55 pm

Ah my mistake I did not see 19.15 Thanks.
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