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