BÉLGICAAR(1)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:42Sample (adjusted): 1961 2015Included observations: 55 after adjustmentsConvergence achieved after 2 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 2.03E+11 1.33E+12 0.152605 0.8793AR(1) 0.997431 0.020692 48.20277 0.0000
R-squared 0.977750 Mean dependent var 2.03E+11Adjusted R-squared 0.977330 S.D. dependent var 1.69E+11S.E. of regression 2.54E+10 Akaike info criterion 50.78996Sum squared resid 3.42E+22 Schwarz criterion 50.86295Log likelihood -1394.724 Hannan-Quinn criter. 50.81819F-statistic 2328.992 Durbin-Watson stat 1.292063Prob(F-statistic) 0.000000
Inverted AR Roots 1.00
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de AR(1) es de 0,997431 con un t-student de 48,20277 lo cual quiere decir que el coeficiente es significativo
Con la bondad de ajuste se puede ver que el modelo explica un 97,775% del comportamiento de la variable y que el modelo en general si es significativo
AR(2)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:44Sample (adjusted): 1962 2015Included observations: 54 after adjustmentsConvergence achieved after 3 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 2.06E+11 2.53E+11 0.816593 0.4180AR(1) 1.331953 0.163747 8.134200 0.0000AR(2) -0.346785 0.168444 -2.058754 0.0446
R-squared 0.979348 Mean dependent var 2.06E+11Adjusted R-squared 0.978538 S.D. dependent var 1.68E+11S.E. of regression 2.46E+10 Akaike info criterion 50.74780Sum squared resid 3.10E+22 Schwarz criterion 50.85829Log likelihood -1367.190 Hannan-Quinn criter. 50.79041F-statistic 1209.255 Durbin-Watson stat 1.784010Prob(F-statistic) 0.000000
Inverted AR Roots .98 .35
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de AR(1) es de 1,331953 con un t-student de 8,1342 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de AR(2) es de -0,346785 con un t-student de -2,058754 lo cual quiere decir que el coeficiente es no significativo para el modelo
Con la bondad de ajuste se puede ver que el modelo explica un 97,9348% del comportamiento de la variable y que el modelo en general si es significativo AR(3)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:45Sample (adjusted): 1963 2015Included observations: 53 after adjustmentsConvergence achieved after 3 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 2.10E+11 2.90E+11 0.723364 0.4729AR(1) 1.350554 0.169444 7.970524 0.0000AR(2) -0.421884 0.262122 -1.609495 0.1139AR(3) 0.057066 0.174796 0.326472 0.7455
R-squared 0.978887 Mean dependent var 2.10E+11Adjusted R-squared 0.977595 S.D. dependent var 1.68E+11S.E. of regression 2.51E+10 Akaike info criterion 50.80272Sum squared resid 3.09E+22 Schwarz criterion 50.95142Log likelihood -1342.272 Hannan-Quinn criter. 50.85990F-statistic 757.2874 Durbin-Watson stat 1.775317Prob(F-statistic) 0.000000
Inverted AR Roots .98 .19+.15i .19-.15i
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de AR(1) es de 1,350554 con un t-student de 7,970524 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de AR(2) es de -0,421884 con un t-student de -1,609495 lo cual quiere decir que el coeficiente es no significativo para el modeloEl coeficiente de AR(3) es de 0,057066 con un t-student de 0,326472 lo cual quiere decir que el coeficiente es no significativo para el modelo
Con la bondad de ajuste se puede ver que el modelo explica un 97,8887% del comportamiento de la variable y que el modelo en general si es significativo
AR(4)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:46Sample (adjusted): 1964 2015Included observations: 52 after adjustmentsConvergence achieved after 3 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 2.14E+11 1.57E+11 1.362003 0.1797AR(1) 1.356941 0.157795 8.599382 0.0000AR(2) -0.595054 0.247601 -2.403282 0.0202AR(3) 0.707133 0.248172 2.849368 0.0065AR(4) -0.495637 0.162710 -3.046136 0.0038
R-squared 0.982414 Mean dependent var 2.14E+11Adjusted R-squared 0.980917 S.D. dependent var 1.67E+11S.E. of regression 2.31E+10 Akaike info criterion 50.65325Sum squared resid 2.50E+22 Schwarz criterion 50.84087Log likelihood -1311.985 Hannan-Quinn criter. 50.72518F-statistic 656.3908 Durbin-Watson stat 1.828778Prob(F-statistic) 0.000000
Inverted AR Roots .91+.07i .91-.07i -.23+.74i -.23-.74i
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de AR(1) es de 1,356941 con un t-student de 8,599382 lo cual quiere decir que el coeficiente es significativo para el modelo.
El coeficiente de AR(2) es de -0,595054 con un t-student de -2,403282 lo cual quiere decir que el coeficiente es no significativo para el modeloEl coeficiente de AR(3) es de 0,707133 con un t-student de -3,046136 lo cual quiere decir que el coeficiente es no significativo para el modeloEl coeficiente de AR(4) es de -0,495637con un t-student de -3,046136 lo cual quiere decir que el coeficiente es no significativo para el modeloCon la bondad de ajuste se puede ver que el modelo explica un 98,2414% del comportamiento de la variable y que el modelo en general si es significativo
AR(5)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:51Sample (adjusted): 1965 2015Included observations: 51 after adjustmentsConvergence achieved after 3 iterations
Variable Coefficient Std. Error t-Statistic Prob.
C 2.18E+11 1.87E+11 1.166924 0.2494AR(1) 1.381862 0.165007 8.374544 0.0000AR(2) -0.630899 0.263430 -2.394939 0.0208AR(3) 0.746543 0.266759 2.798568 0.0075AR(4) -0.601254 0.276978 -2.170762 0.0353AR(5) 0.078739 0.184710 0.426283 0.6719
R-squared 0.982019 Mean dependent var 2.18E+11Adjusted R-squared 0.980021 S.D. dependent var 1.66E+11S.E. of regression 2.35E+10 Akaike info criterion 50.70940Sum squared resid 2.49E+22 Schwarz criterion 50.93667Log likelihood -1287.090 Hannan-Quinn criter. 50.79625F-statistic 491.5277 Durbin-Watson stat 1.892221Prob(F-statistic) 0.000000
Inverted AR Roots .89-.03i .89+.03i .16 -.28-.74i-.28+.74i
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
1965 1970 1975 1980 1985 1990 1995 2000 2005 2010 2015
Residual Actual Fitted
El coeficiente de AR(1) es de 1,381862 con un t-student de 8,374544 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de AR(2) es de -0,630899 con un t-student de -2,394939 lo cual quiere decir que el coeficiente es no significativo para el modeloEl coeficiente de AR(3) es de 0,746543 con un t-student de 2,798568 lo cual quiere decir que el coeficiente es significativo para el modeloEl coeficiente de AR(4) es de -0,601254 con un t-student de -2.170762lo cual quiere decir que el coeficiente es no significativo para el modeloEl coeficiente de AR(5) es de 0.078739 con un t-student de 0.426283 lo cual quiere decir que el coeficiente es no significativo para el modelo
Con la bondad de ajuste se puede ver que el modelo explica un 98,2018% del comportamiento de la variable y que el modelo en general si es significativo
MA(1)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:55Sample: 1960 2015Included observations: 56Convergence achieved after 11 iterationsMA Backcast: 1959
Variable Coefficient Std. Error t-Statistic Prob.
C 2.00E+11 2.34E+10 8.539859 0.0000MA(1) 0.966187 0.027391 35.27379 0.0000
R-squared 0.727482 Mean dependent var 2.00E+11Adjusted R-squared 0.722435 S.D. dependent var 1.69E+11S.E. of regression 8.91E+10 Akaike info criterion 53.29910Sum squared resid 4.29E+23 Schwarz criterion 53.37144Log likelihood -1490.375 Hannan-Quinn criter. 53.32715F-statistic 144.1518 Durbin-Watson stat 0.197409Prob(F-statistic) 0.000000
Inverted MA Roots -.97
-1.0E+11
-5.0E+10
0.0E+00
5.0E+10
1.0E+11
1.5E+11
2.0E+11
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
60 65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de MA(1) es de 0,966187 con un t-student de 35.27379 lo cual quiere decir que el coeficiente es significativo para el modelo.Con la bondad de ajuste se puede ver que el modelo explica un 72,7482% del comportamiento de la variable
MA(2)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:57Sample: 1960 2015Included observations: 56Convergence achieved after 14 iterationsMA Backcast: 1958 1959
Variable Coefficient Std. Error t-Statistic Prob.
C 2.00E+11 2.54E+10 7.840497 0.0000MA(1) 1.617492 0.031704 51.01821 0.0000MA(2) 0.922551 0.031906 28.91444 0.0000
R-squared 0.902071 Mean dependent var 2.00E+11Adjusted R-squared 0.898375 S.D. dependent var 1.69E+11S.E. of regression 5.39E+10 Akaike info criterion 52.31136Sum squared resid 1.54E+23 Schwarz criterion 52.41986Log likelihood -1461.718 Hannan-Quinn criter. 52.35342F-statistic 244.1030 Durbin-Watson stat 0.641765Prob(F-statistic) 0.000000
Inverted MA Roots -.81-.52i -.81+.52i
-8.0E+10
-4.0E+10
0.0E+00
4.0E+10
8.0E+10
1.2E+11
1.6E+11
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
60 65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de MA(1) es de 1.617492 con un t-student de 51.01821 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de MA(2) es de 0.922551 con un t-student de 28.91444 lo cual quiere decir que el coeficiente es significativo para el modeloCon la bondad de ajuste se puede ver que el modelo explica un 90,2071% del comportamiento de la variable
MA(3)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:58Sample: 1960 2015Included observations: 56Convergence achieved after 10 iterationsMA Backcast: 1957 1959
Variable Coefficient Std. Error t-Statistic Prob.
C 2.00E+11 3.13E+10 6.384873 0.0000MA(1) 2.022746 0.086501 23.38408 0.0000MA(2) 1.904226 0.111212 17.12246 0.0000MA(3) 0.767948 0.080360 9.556300 0.0000
R-squared 0.943966 Mean dependent var 2.00E+11Adjusted R-squared 0.940733 S.D. dependent var 1.69E+11S.E. of regression 4.12E+10 Akaike info criterion 51.78879Sum squared resid 8.82E+22 Schwarz criterion 51.93345Log likelihood -1446.086 Hannan-Quinn criter. 51.84487F-statistic 292.0023 Durbin-Watson stat 1.508163Prob(F-statistic) 0.000000
Inverted MA Roots -.59+.75i -.59-.75i -.84
-5.0E+10
0.0E+00
5.0E+10
1.0E+11
1.5E+11
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
60 65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de MA(1) es de 2.022746 con un t-student de 23.38408 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de MA(2) es de 1.904226 con un t-student de 17.12246 lo cual quiere decir que el coeficiente es significativo para el modeloEl coeficiente de MA(3) es de 0.767948 con un t-student de 9.556300 lo cual quiere decir que el coeficiente es significativo para el modeloCon la bondad de ajuste se puede ver que el modelo explica un 94,,3966% del comportamiento de la variable y que el modelo en general si es significativo MA(4)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:59Sample: 1960 2015Included observations: 56Convergence achieved after 34 iterationsMA Backcast: 1956 1959
Variable Coefficient Std. Error t-Statistic Prob.
C 2.11E+11 3.68E+10 5.727418 0.0000MA(1) 2.029627 0.095131 21.33500 0.0000MA(2) 2.288265 0.156511 14.62043 0.0000MA(3) 1.816358 0.145177 12.51136 0.0000MA(4) 0.747654 0.088499 8.448148 0.0000
R-squared 0.960399 Mean dependent var 2.00E+11Adjusted R-squared 0.957293 S.D. dependent var 1.69E+11S.E. of regression 3.50E+10 Akaike info criterion 51.47740Sum squared resid 6.23E+22 Schwarz criterion 51.65823Log likelihood -1436.367 Hannan-Quinn criter. 51.54750F-statistic 309.2113 Durbin-Watson stat 1.789542Prob(F-statistic) 0.000000
Inverted MA Roots -.16-.94i -.16+.94i -.85+.31i -.85-.31i
-8.0E+10
-4.0E+10
0.0E+00
4.0E+10
8.0E+10
1.2E+11
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
60 65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de MA(1) es de 2.029627 con un t-student de 21.33500 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de MA(2) es de 2.288265 con un t-student de 14.62043 lo cual quiere decir que el coeficiente essignificativo para el modeloEl coeficiente de MA(3) es de 1.816358 con un t-student de 12.51136 lo cual quiere decir que el coeficiente es significativo para el modeloEl coeficiente de MA(4) es de 0.747654 con un t-student de 8.448148 lo cual quiere decir que el coeficiente es significativo para el modeloCon la bondad de ajuste se puede ver que el modelo explica un 96,0399% del comportamiento de la variable y que el modelo en general si es significativo
MA(5)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 19:59Sample: 1960 2015Included observations: 56Convergence achieved after 38 iterationsMA Backcast: 1955 1959
Variable Coefficient Std. Error t-Statistic Prob.
C 2.15E+11 3.38E+10 6.361897 0.0000MA(1) 1.713659 0.113948 15.03890 0.0000MA(2) 1.614188 0.158075 10.21151 0.0000MA(3) 1.615126 0.135711 11.90126 0.0000MA(4) 1.503750 0.132362 11.36090 0.0000MA(5) 0.624692 0.104744 5.964003 0.0000
R-squared 0.968729 Mean dependent var 2.00E+11Adjusted R-squared 0.965602 S.D. dependent var 1.69E+11S.E. of regression 3.14E+10 Akaike info criterion 51.27694Sum squared resid 4.92E+22 Schwarz criterion 51.49394Log likelihood -1429.754 Hannan-Quinn criter. 51.36107F-statistic 309.7864 Durbin-Watson stat 1.545692Prob(F-statistic) 0.000000
Inverted MA Roots .29-.92i .29+.92i -.75-.52i -.75+.52i -.81
-8.0E+10
-4.0E+10
0.0E+00
4.0E+10
8.0E+10
1.2E+11
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
60 65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
El coeficiente de MA(1) es de 1.713659 con un t-student de 15.03890 lo cual quiere decir que el coeficiente es significativo para el modelo.El coeficiente de MA(2) es de 1.614188 con un t-student de 10.21151 lo cual quiere decir que el coeficiente essignificativo para el modeloEl coeficiente de MA(3) es de 1.615126 con un t-student de 11.90126 lo cual quiere decir que el coeficiente es significativo para el modelo
El coeficiente de MA(4) es de 1.503750 con un t-student de 11.36090 lo cual quiere decir que el coeficiente es significativo para el modeloEl coeficiente de MA(5) es de 0.624692 con un t-student de 5.964003 lo cual quiere decir que el coeficiente es significativo para el modelo
Con la bondad de ajuste se puede ver que el modelo explica un 96,8729% del comportamiento de la variable y que el modelo en general si es significativo
ARMA(1,1)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:05Sample (adjusted): 1961 2015Included observations: 55 after adjustmentsConvergence achieved after 8 iterationsMA Backcast: 1960
Variable Coefficient Std. Error t-Statistic Prob.
C 2.03E+11 2.47E+11 0.820500 0.4157AR(1) 0.979643 0.030029 32.62346 0.0000MA(1) 0.568317 0.117741 4.826849 0.0000
R-squared 0.981005 Mean dependent var 2.03E+11Adjusted R-squared 0.980274 S.D. dependent var 1.69E+11S.E. of regression 2.37E+10 Akaike info criterion 50.66817Sum squared resid 2.92E+22 Schwarz criterion 50.77766Log likelihood -1390.375 Hannan-Quinn criter. 50.71051F-statistic 1342.753 Durbin-Watson stat 2.027391Prob(F-statistic) 0.000000
Inverted AR Roots .98Inverted MA Roots -.57
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(1,2)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:06Sample (adjusted): 1961 2015Included observations: 55 after adjustmentsConvergence achieved after 49 iterationsMA Backcast: 1959 1960
Variable Coefficient Std. Error t-Statistic Prob.
C 7.41E+11 1.10E+12 0.673408 0.5037AR(1) 0.986388 0.026087 37.81152 0.0000MA(1) 0.406931 0.165324 2.461419 0.0173MA(2) -0.188325 0.173506 -1.085406 0.2828
R-squared 0.982552 Mean dependent var 2.03E+11Adjusted R-squared 0.981525 S.D. dependent var 1.69E+11S.E. of regression 2.29E+10 Akaike info criterion 50.61957Sum squared resid 2.68E+22 Schwarz criterion 50.76556Log likelihood -1388.038 Hannan-Quinn criter. 50.67603F-statistic 957.3114 Durbin-Watson stat 1.884290Prob(F-statistic) 0.000000
Inverted AR Roots .99Inverted MA Roots .28 -.68
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(1,3)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:13Sample (adjusted): 1961 2015Included observations: 55 after adjustmentsConvergence achieved after 49 iterationsMA Backcast: 1958 1960
Variable Coefficient Std. Error t-Statistic Prob.
C 9.39E+11 2.05E+12 0.458458 0.6486AR(1) 0.989793 0.027394 36.13167 0.0000MA(1) 0.209088 0.153248 1.364375 0.1786MA(2) -0.104196 0.161899 -0.643587 0.5228MA(3) 0.309204 0.156570 1.974854 0.0538
R-squared 0.983200 Mean dependent var 2.03E+11Adjusted R-squared 0.981856 S.D. dependent var 1.69E+11S.E. of regression 2.27E+10 Akaike info criterion 50.61807Sum squared resid 2.58E+22 Schwarz criterion 50.80056Log likelihood -1386.997 Hannan-Quinn criter. 50.68864F-statistic 731.5495 Durbin-Watson stat 1.700158Prob(F-statistic) 0.000000
Inverted AR Roots .99Inverted MA Roots .30+.54i .30-.54i -.81
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(1,4)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:14Sample (adjusted): 1961 2015Included observations: 55 after adjustmentsConvergence achieved after 13 iterationsMA Backcast: 1957 1960
Variable Coefficient Std. Error t-Statistic Prob.
C 2.03E+11 1.58E+11 1.284443 0.2050AR(1) 0.951114 0.043064 22.08612 0.0000MA(1) 0.388999 0.115206 3.376544 0.0014MA(2) -0.031866 0.072222 -0.441223 0.6610MA(3) 0.681803 0.065056 10.48029 0.0000MA(4) 0.615560 0.112452 5.473978 0.0000
R-squared 0.985338 Mean dependent var 2.03E+11Adjusted R-squared 0.983842 S.D. dependent var 1.69E+11S.E. of regression 2.14E+10 Akaike info criterion 50.51831Sum squared resid 2.25E+22 Schwarz criterion 50.73729Log likelihood -1383.253 Hannan-Quinn criter. 50.60299F-statistic 658.6037 Durbin-Watson stat 1.925772Prob(F-statistic) 0.000000
Inverted AR Roots .95Inverted MA Roots .55+.80i .55-.80i -.74-.32i -.74+.32i
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(2,1)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:17Sample (adjusted): 1962 2015Included observations: 54 after adjustmentsConvergence achieved after 48 iterationsMA Backcast: 1961
Variable Coefficient Std. Error t-Statistic Prob.
C 1.16E+12 2.99E+12 0.389081 0.6989AR(1) 0.627106 0.290800 2.156485 0.0359AR(2) 0.361754 0.295137 1.225716 0.2260MA(1) 0.747744 0.196734 3.800788 0.0004
R-squared 0.982200 Mean dependent var 2.06E+11Adjusted R-squared 0.981132 S.D. dependent var 1.68E+11S.E. of regression 2.31E+10 Akaike info criterion 50.63624Sum squared resid 2.67E+22 Schwarz criterion 50.78358Log likelihood -1363.179 Hannan-Quinn criter. 50.69306F-statistic 919.6453 Durbin-Watson stat 1.885894Prob(F-statistic) 0.000000
Inverted AR Roots .99 -.36Inverted MA Roots -.75
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(2,2)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:18Sample (adjusted): 1962 2015Included observations: 54 after adjustmentsConvergence achieved after 18 iterationsMA Backcast: 1960 1961
Variable Coefficient Std. Error t-Statistic Prob.
C 2.06E+11 3.91E+11 0.527874 0.6000AR(1) 0.745200 1.227120 0.607276 0.5465AR(2) 0.238487 1.200473 0.198661 0.8433MA(1) 0.700441 1.252371 0.559292 0.5785MA(2) -0.005587 0.729579 -0.007658 0.9939
R-squared 0.980963 Mean dependent var 2.06E+11Adjusted R-squared 0.979409 S.D. dependent var 1.68E+11S.E. of regression 2.41E+10 Akaike info criterion 50.74043Sum squared resid 2.86E+22 Schwarz criterion 50.92460Log likelihood -1364.992 Hannan-Quinn criter. 50.81146F-statistic 631.2451 Durbin-Watson stat 1.872494Prob(F-statistic) 0.000000
Inverted AR Roots .99 -.24Inverted MA Roots .01 -.71
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(2,3)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:19Sample (adjusted): 1962 2015Included observations: 54 after adjustmentsConvergence achieved after 263 iterationsWARNING: Singular covariance - coefficients are not uniqueMA Backcast: OFF (Roots of MA process too large)
Variable Coefficient Std. Error t-Statistic Prob.
C 2.06E+11 NA NA NAAR(1) 0.501850 NA NA NAAR(2) 0.490029 NA NA NAMA(1) 0.983631 NA NA NAMA(2) -0.032672 NA NA NAMA(3) 0.444045 NA NA NA
R-squared 0.986828 Mean dependent var 2.06E+11Adjusted R-squared 0.985455 S.D. dependent var 1.68E+11S.E. of regression 2.03E+10 Akaike info criterion 50.40923Sum squared resid 1.98E+22 Schwarz criterion 50.63023Log likelihood -1355.049 Hannan-Quinn criter. 50.49446F-statistic 719.1929 Durbin-Watson stat 1.474103Prob(F-statistic) 0.000000
Inverted AR Roots .99 -.49Inverted MA Roots .15-.57i .15+.57i -1.28
Estimated MA process is noninvertible
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(2,4)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:21Sample (adjusted): 1962 2015Included observations: 54 after adjustmentsConvergence achieved after 13 iterationsMA Backcast: 1958 1961
Variable Coefficient Std. Error t-Statistic Prob.
C 2.06E+11 1.65E+11 1.248191 0.2181AR(1) 0.866350 0.275943 3.139601 0.0029AR(2) 0.082683 0.279356 0.295976 0.7686MA(1) 0.446596 0.198478 2.250104 0.0292MA(2) -0.027905 0.077709 -0.359089 0.7211MA(3) 0.689476 0.065377 10.54611 0.0000MA(4) 0.649295 0.164786 3.940238 0.0003
R-squared 0.985011 Mean dependent var 2.06E+11Adjusted R-squared 0.983097 S.D. dependent var 1.68E+11S.E. of regression 2.19E+10 Akaike info criterion 50.57546Sum squared resid 2.25E+22 Schwarz criterion 50.83329Log likelihood -1358.537 Hannan-Quinn criter. 50.67490F-statistic 514.7678 Durbin-Watson stat 1.889987Prob(F-statistic) 0.000000
Inverted AR Roots .95 -.09Inverted MA Roots .54+.80i .54-.80i -.77-.32i -.77+.32i
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(3,1)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:24Sample (adjusted): 1963 2015Included observations: 53 after adjustmentsConvergence achieved after 16 iterationsMA Backcast: 1962
Variable Coefficient Std. Error t-Statistic Prob.
C 2.10E+11 3.67E+11 0.572758 0.5695AR(1) 0.738803 0.341427 2.163866 0.0355AR(2) 0.236683 0.508328 0.465611 0.6436AR(3) 0.006695 0.256463 0.026106 0.9793MA(1) 0.705447 0.292344 2.413071 0.0197
R-squared 0.980485 Mean dependent var 2.10E+11Adjusted R-squared 0.978859 S.D. dependent var 1.68E+11S.E. of regression 2.44E+10 Akaike info criterion 50.76175Sum squared resid 2.85E+22 Schwarz criterion 50.94762Log likelihood -1340.186 Hannan-Quinn criter. 50.83322F-statistic 602.9174 Durbin-Watson stat 1.870402Prob(F-statistic) 0.000000
Inverted AR Roots .99 -.03 -.22Inverted MA Roots -.71
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(3,2)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:25Sample (adjusted): 1963 2015Included observations: 53 after adjustmentsConvergence achieved after 22 iterationsMA Backcast: 1961 1962
Variable Coefficient Std. Error t-Statistic Prob.
C 2.10E+11 2.31E+11 0.909481 0.3677AR(1) 1.577792 0.303572 5.197415 0.0000AR(2) -0.190766 0.606228 -0.314677 0.7544AR(3) -0.396600 0.334372 -1.186104 0.2415MA(1) -0.206671 0.207579 -0.995629 0.3245MA(2) -0.725382 0.202853 -3.575894 0.0008
R-squared 0.982310 Mean dependent var 2.10E+11Adjusted R-squared 0.980428 S.D. dependent var 1.68E+11S.E. of regression 2.35E+10 Akaike info criterion 50.70133Sum squared resid 2.59E+22 Schwarz criterion 50.92438Log likelihood -1337.585 Hannan-Quinn criter. 50.78710F-statistic 521.9613 Durbin-Watson stat 1.938292Prob(F-statistic) 0.000000
Inverted AR Roots .99-.08i .99+.08i -.40Inverted MA Roots .96 -.75
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(3,3)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:25Sample (adjusted): 1963 2015Included observations: 53 after adjustmentsConvergence achieved after 30 iterationsMA Backcast: 1960 1962
Variable Coefficient Std. Error t-Statistic Prob.
C 5.37E+11 5.06E+11 1.062563 0.2935AR(1) 1.573148 0.183435 8.576041 0.0000AR(2) -1.008485 0.316614 -3.185221 0.0026AR(3) 0.414744 0.182122 2.277286 0.0275MA(1) -0.355451 0.136537 -2.603319 0.0124MA(2) 0.165885 0.143578 1.155365 0.2539MA(3) 0.659560 0.122993 5.362597 0.0000
R-squared 0.984796 Mean dependent var 2.10E+11Adjusted R-squared 0.982813 S.D. dependent var 1.68E+11S.E. of regression 2.20E+10 Akaike info criterion 50.58759Sum squared resid 2.22E+22 Schwarz criterion 50.84782Log likelihood -1333.571 Hannan-Quinn criter. 50.68766F-statistic 496.5908 Durbin-Watson stat 1.807474
Prob(F-statistic) 0.000000
Inverted AR Roots .98 .30+.58i .30-.58iInverted MA Roots .53+.80i .53-.80i -.71
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(3,4)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:26Sample (adjusted): 1963 2015Included observations: 53 after adjustmentsConvergence achieved after 32 iterationsMA Backcast: 1959 1962
Variable Coefficient Std. Error t-Statistic Prob.
C 4.19E+11 2.97E+11 1.411318 0.1650AR(1) 0.891892 0.338838 2.632211 0.0116AR(2) -0.034407 0.519879 -0.066183 0.9475AR(3) 0.096719 0.262707 0.368163 0.7145MA(1) 0.383235 0.283726 1.350720 0.1835MA(2) -0.007255 0.116402 -0.062328 0.9506MA(3) 0.681654 0.073056 9.330504 0.0000MA(4) 0.614544 0.227540 2.700817 0.0097
R-squared 0.985108 Mean dependent var 2.10E+11Adjusted R-squared 0.982792 S.D. dependent var 1.68E+11S.E. of regression 2.20E+10 Akaike info criterion 50.60459Sum squared resid 2.18E+22 Schwarz criterion 50.90199Log likelihood -1333.022 Hannan-Quinn criter. 50.71895F-statistic 425.2585 Durbin-Watson stat 1.890945
Prob(F-statistic) 0.000000
Inverted AR Roots .96 -.03-.32i -.03+.32iInverted MA Roots .54-.81i .54+.81i -.74-.33i -.74+.33i
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(4,1)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:29Sample (adjusted): 1964 2015Included observations: 52 after adjustmentsConvergence achieved after 7 iterationsMA Backcast: 1963
Variable Coefficient Std. Error t-Statistic Prob.
C 2.14E+11 1.86E+11 1.147476 0.2571AR(1) 1.167331 0.365569 3.193187 0.0025AR(2) -0.338161 0.484414 -0.698081 0.4886AR(3) 0.626695 0.282573 2.217821 0.0315AR(4) -0.484398 0.179124 -2.704261 0.0096MA(1) 0.223870 0.355196 0.630273 0.5316
R-squared 0.982534 Mean dependent var 2.14E+11Adjusted R-squared 0.980636 S.D. dependent var 1.67E+11S.E. of regression 2.32E+10 Akaike info criterion 50.68486Sum squared resid 2.49E+22 Schwarz criterion 50.91000Log likelihood -1311.806 Hannan-Quinn criter. 50.77117F-statistic 517.5391 Durbin-Watson stat 1.918709Prob(F-statistic) 0.000000
Inverted AR Roots .91 .86 -.30-.73i -.30+.73iInverted MA Roots -.22
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(4,2)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:31Sample (adjusted): 1964 2015Included observations: 52 after adjustmentsConvergence achieved after 35 iterationsMA Backcast: 1962 1963
Variable Coefficient Std. Error t-Statistic Prob.
C 4.90E+11 6.01E+11 0.815297 0.4192AR(1) 0.983955 0.522034 1.884850 0.0659AR(2) -0.190451 0.489024 -0.389450 0.6988AR(3) 0.584666 0.455427 1.283777 0.2058AR(4) -0.399348 0.198642 -2.010395 0.0504MA(1) 0.360453 0.525610 0.685781 0.4964MA(2) 0.023361 0.483815 0.048286 0.9617
R-squared 0.982906 Mean dependent var 2.14E+11Adjusted R-squared 0.980627 S.D. dependent var 1.67E+11S.E. of regression 2.33E+10 Akaike info criterion 50.70178Sum squared resid 2.43E+22 Schwarz criterion 50.96445Log likelihood -1311.246 Hannan-Quinn criter. 50.80248F-statistic 431.2566 Durbin-Watson stat 1.890921
Prob(F-statistic) 0.000000
Inverted AR Roots .97 .67 -.33+.71i -.33-.71iInverted MA Roots -.08 -.28
-8E+10
-4E+10
0E+00
4E+10
8E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(4,3)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:31Sample (adjusted): 1964 2015Included observations: 52 after adjustmentsConvergence achieved after 49 iterationsMA Backcast: 1961 1963
Variable Coefficient Std. Error t-Statistic Prob.
C 4.06E+11 4.83E+11 0.839038 0.4060AR(1) 0.816190 0.545533 1.496132 0.1418AR(2) 0.052634 0.584095 0.090111 0.9286AR(3) 0.649974 0.434737 1.495098 0.1420AR(4) -0.544663 0.373665 -1.457621 0.1520MA(1) 0.544886 0.550722 0.989403 0.3279MA(2) 0.012699 0.679663 0.018684 0.9852MA(3) -0.202548 0.471936 -0.429186 0.6699
R-squared 0.983053 Mean dependent var 2.14E+11Adjusted R-squared 0.980357 S.D. dependent var 1.67E+11S.E. of regression 2.34E+10 Akaike info criterion 50.73161Sum squared resid 2.41E+22 Schwarz criterion 51.03181Log likelihood -1311.022 Hannan-Quinn criter. 50.84670F-statistic 364.6206 Durbin-Watson stat 1.929258
Prob(F-statistic) 0.000000
Inverted AR Roots .96 .75 -.45+.75i -.45-.75iInverted MA Roots .45 -.50+.46i -.50-.46i
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
ARMA(4,4)
Dependent Variable: PIBMethod: Least SquaresDate: 03/03/17 Time: 20:32Sample (adjusted): 1964 2015Included observations: 52 after adjustmentsConvergence achieved after 32 iterationsMA Backcast: 1960 1963
Variable Coefficient Std. Error t-Statistic Prob.
C 5.19E+11 5.16E+11 1.005870 0.3201AR(1) 0.694086 0.259173 2.678083 0.0104AR(2) 0.261626 0.384522 0.680391 0.4999AR(3) -0.219026 0.360653 -0.607305 0.5468AR(4) 0.223727 0.236641 0.945431 0.3497MA(1) 0.572893 0.204244 2.804948 0.0075MA(2) -0.065672 0.105551 -0.622188 0.5371MA(3) 0.750655 0.080520 9.322620 0.0000MA(4) 0.716196 0.147784 4.846224 0.0000
R-squared 0.985108 Mean dependent var 2.14E+11Adjusted R-squared 0.982338 S.D. dependent var 1.67E+11S.E. of regression 2.22E+10 Akaike info criterion 50.64080Sum squared resid 2.12E+22 Schwarz criterion 50.97851Log likelihood -1307.661 Hannan-Quinn criter. 50.77027
F-statistic 355.5636 Durbin-Watson stat 1.889651Prob(F-statistic) 0.000000
Inverted AR Roots .97 .22+.52i .22-.52i -.71Inverted MA Roots .54+.81i .54-.81i -.82+.28i -.82-.28i
-6E+10
-4E+10
-2E+10
0E+00
2E+10
4E+10
6E+10
0E+00
1E+11
2E+11
3E+11
4E+11
5E+11
6E+11
65 70 75 80 85 90 95 00 05 10 15
Residual Actual Fitted
AKAIKE SCHWARZHANNAN-QUINN R² F-statistic
ARMA(1,1) 50,66817 50,77766 50,71051 0.981005 1342,753ARMA(1,2) 50,61957 50,76556 50,67603 0.982552 957,3114ARMA(1,3) 50,61807 50,80056 50,68864 0.983200 731,5495ARMA(1,4) 50,51831 50,73729 50,60299 0.985338 658,6037ARMA(2,1) 50,63624 50,78358 50,69306 0.982200 919,6453ARMA(2,2) 50,74043 50,9246 50,81146 0.980963 631,2451ARMA(2,3) 50,40923 50,63023 50,49446 0.986828 719,1929ARMA(2,4) 50,57546 50,83329 50,6749 0.985011 514,7678ARMA(3,1) 50,76175 50,94762 50,83322 0.980485 602,9174ARMA(3,2) 50,70133 50,92438 50,7871 0.982310 521,9613ARMA(3,3) 50,58759 50,84782 50,68766 0.984796 496,5908ARMA(3,4) 50,60459 50,90199 50,71895 0.985108 425,2585ARMA(4,1) 50,68486 50,91 50,77117 0.982534 517,5391ARMA(4,2) 50,70178 50,96445 50,80248 0.982906 431,2566ARMA(4,3) 50,73161 51,03181 50,8467 0.983053 364,6206ARMA(4,4) 50,6408 50,97851 50,77027 0.985108 355,5636
El ARMA(2,3) es el adecuado desde el punto de vista de AKAIKE Y R²