TAREA Nº 4 ECONOMETRIA II

MODELO AR(p), MA(q) Y ARMA(p.q)

En el siguiente trabajo se seleccionara 3 variables económicas de Suiza, sobre las cuales se

estimara los modelos AR(p), MA(q) y ARMA(pq) hasta el nivel 3, utilizando el programa

Eviews.

Se seleccionó las siguientes variables económicas:

Ingreso nacional bruto expresado en miles de millones de $us a precios actuales desde

1961 hasta el 2016.

Importaciones expresado en miles de millones de $us a precios actuales desde 1961

hasta el 2016.

PIB expresado en miles de millones de $us a precios actuales desde 1961 hasta el

2016.

BASE DE DATOS

AÑO PIB IMPORTACIO

NES DE SUIZA INB2016 659.850 268,658 658,1682015 670.656 253,11 660,3332014 702.736 275,742 649,8032013 685.104 321,509 649,6062012 664.902 295,961 637,5892011 696.447 208,22 624,3092010 580.607 176,281 642,8272009 540.966 155,378 599,1242008 552.287 183,574 558,9912007 477.784 161,18 577,352006 429.477 141,4 579,1582005 407.592 126,574 550,8162004 393.038 115,799 520,4722003 352.356 100,239 505,8522002 301.321 87,189 482,4292001 278.821 84,102 488,9372000 271.852 82,521 489,3471999 289.600 79,857 460,4441998 294.750 80,094 448,9171997 286.673 75,96 434,9581996 329.762 78,224 418,9561995 341.958 80,152 414,5391994 291.883 67,997 406,091993 263.445 60,828 399,591992 271.053 65,723 389,2411991 260.542 66,485 382,3841990 257.544 69,681 365,7911989 201.666 58,194 340,6151988 208.800 56,363 317,5521987 192.949 50,652 296,9011986 154.151 41,051 287,4891985 107.580 30,696 277,0361984 106.025 29,522 261,8721983 110.993 29,192 243,411982 111.313 28,678 235,2571981 108.674 30,697 224,0811980 118.714 36,341 206,8381979 105.565 29,356 192,6621978 93.913 23,804 183,6871977 67.153 17,94 177,1621976 62.875 14,775 171,6571975 60.111 13,303 168,6771974 52.432 14,445 170,5851973 45.497 11,626 156,9151972 33.830 8,468 140,581971 27.583 7,191 124,1941970 22.953 6,374 109,5511969 20.525 5,199 90,8571968 18.943 4,442 83,7531967 17.740 4,067 78,0591966 16.480 3,888 72,5021965 15.347 3,643 67,3321964 14.481 3,554 64,2971963 13.064 3,199 58,0961962 11.880 2,97 52,9581961 10.713 2,663 47,829

VARIABLE Nº 1 “PIB” MODELO AR(P)

Con la variable económica INB se realizara el modelo AR(p)

TEST DE LA RAÍZ UNITARIA PARA DETECTAR SIN EL MODELO ES NO ESTACIONARIO

AR(1)

Modelo del PIB sin la corrección

Modelo AR(1) ya corregido

AR(2)

Modelo sin corregir

Modelo corregido

AR(3)

Modelo sin corregir

Modelo corregido

MODELO ARMA (p,q)

ARMA (1.1)

Modelo del PIB sin la corrección

Modelo corregido

ARMA (1.2)

Modelo del PIB sin la corrección

Modelo corregido

ARMA (1.3)

Modelo corregido

ARMA (2.1)

Modelo corregido

ARMA (2.2)

Modelo corregido

ARMA (2.3)

Modelo corregido

ARMA (3.1)

Modelo corregido

ARMA (3.2)

Modelo corregido

ARMA (3.3)

Modelo corregido

VARIABLE Nº 2 “INB”

MODELO AR(P)

AR(1)

Modelo corregido

AR(2)

Modelo corregido

AR(3)

Modelo corregido

MODELO ARMA(p,q)

ARMA(1.1)

Modelo corregido

ARMA(1.2)

Modelo corregido

ARMA(1.3)

Modelo corregido

ARMA(2.1)

Modelo corregido

ARMA(2.2)

Modelo corregido

ARMA(2.3)

Modelo corregido

ARMA(3.1)

Modelo corregido

ARMA(3.2)

Modelo corregido

ARMA(3.3)

Modelo corregido

TEST DE LA RAISUNITARIA PARA DETECTAR SI EL MODELO DE

INB ES NO ESTACIONARIO

Modelo corregido

MODELO DE IMPORTACIONES

KEYNESIANAS

MODELO AR(P) AR(1)

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:11

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 3 iterations Variable Coefficient Std. Error t-Statistic Prob. C 5.041072 3.111253 1.620271 0.1112

AR(1) 0.299936 0.132770 2.259066 0.0281 R-squared 0.089371 Mean dependent var 4.920148

Adjusted R-squared 0.071859 S.D. dependent var 16.60856

S.E. of regression 16.00070 Akaike info criterion 8.419475

Sum squared resid 13313.16 Schwarz criterion 8.493141

Log likelihood -225.3258 Hannan-Quinn criter. 8.447885

F-statistic 5.103381 Durbin-Watson stat 1.734596

Prob(F-statistic) 0.028099 Inverted AR Roots .30

Modelo corregido

AR(2)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:16

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 6 iterations Variable Coefficient Std. Error t-Statistic Prob. C -525.0890 2938.461 -0.178695 0.8589

AR(1) 1.297274 0.134646 9.634735 0.0000

AR(2) -0.291329 0.140509 -2.073388 0.0432 R-squared 0.963827 Mean dependent var 80.16848

Adjusted R-squared 0.962409 S.D. dependent var 83.29819

S.E. of regression 16.15023 Akaike info criterion 8.455699

Sum squared resid 13302.33 Schwarz criterion 8.566198

Log likelihood -225.3039 Hannan-Quinn criter. 8.498314

F-statistic 679.4519 Durbin-Watson stat 1.738303

Prob(F-statistic) 0.000000 Inverted AR Roots 1.01 .29

Estimated AR process is nonstationary

IMPORT = -525.088987471 + [AR(1)=1.29727432923,AR(2)=-0.291329355591]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:18

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 3 iterations Variable Coefficient Std. Error t-Statistic Prob. C 5.198485 2.045004 2.542042 0.0142

AR(1) 0.438172 0.130346 3.361618 0.0015

AR(2) -0.434277 0.133796 -3.245808 0.0021 R-squared 0.247361 Mean dependent var 5.008660

Adjusted R-squared 0.217256 S.D. dependent var 16.75463

S.E. of regression 14.82330 Akaike info criterion 8.285216

Sum squared resid 10986.50 Schwarz criterion 8.396742

Log likelihood -216.5582 Hannan-Quinn criter. 8.328103

F-statistic 8.216470 Durbin-Watson stat 2.166091

Prob(F-statistic) 0.000822 Inverted AR Roots .22-.62i .22+.62i

D(IMPORT) = 5.19848546404 + [AR(1)=0.438171865255,AR(2)=-0.4342774627]

AR(3)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:22

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 4 iterations Variable Coefficient Std. Error t-Statistic Prob. C -47.27268 81.36993 -0.580960 0.5639

AR(1) 1.447531 0.128367 11.27651 0.0000

AR(2) -0.926681 0.214460 -4.321001 0.0001

AR(3) 0.526208 0.143208 3.674424 0.0006 R-squared 0.971188 Mean dependent var 81.62074

Adjusted R-squared 0.969424 S.D. dependent var 83.40231

S.E. of regression 14.58367 Akaike info criterion 8.270154

Sum squared resid 10421.49 Schwarz criterion 8.418855

Log likelihood -215.1591 Hannan-Quinn criter. 8.327337

F-statistic 550.5641 Durbin-Watson stat 2.349485

Prob(F-statistic) 0.000000 Inverted AR Roots 1.04 .20-.68i .20+.68i

Estimated AR process is nonstationary

IMPORT = -47.2726814881 + [AR(1)=1.44753101554,AR(2)=-0.926680718532,AR(3)=0.526208232942]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:21

Sample (adjusted): 1965 2016

Included observations: 52 after adjustments

Convergence achieved after 3 iterations Variable Coefficient Std. Error t-Statistic Prob. C 5.423318 1.659491 3.268061 0.0020

AR(1) 0.354421 0.140854 2.516227 0.0153

AR(2) -0.351717 0.144363 -2.436330 0.0186

AR(3) -0.238401 0.157300 -1.515581 0.1362 R-squared 0.282180 Mean dependent var 5.098154

Adjusted R-squared 0.237317 S.D. dependent var 16.90530

S.E. of regression 14.76369 Akaike info criterion 8.296022

Sum squared resid 10462.39 Schwarz criterion 8.446118

Log likelihood -211.6966 Hannan-Quinn criter. 8.353565

F-statistic 6.289724 Durbin-Watson stat 1.871852

Prob(F-statistic) 0.001095

Inverted AR Roots .37+.70i .37-.70i -.38

D(IMPORT) = 5.42331795317 + [AR(1)=0.354420804353,AR(2)=-0.35171704688,AR(3)=-0.23840110558]

MODELOS ARMA (P,Q)

ARMA (1.1)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:31

Sample (adjusted): 1962 2016

Included observations: 55 after adjustments

Convergence achieved after 70 iterations

MA Backcast: 1961 Variable Coefficient Std. Error t-Statistic Prob. C 10172.92 772949.9 0.013161 0.9895

AR(1) 0.999512 0.037379 26.73965 0.0000

MA(1) 0.418568 0.128838 3.248802 0.0020 R-squared 0.966583 Mean dependent var 78.76487

Adjusted R-squared 0.965298 S.D. dependent var 83.17724

S.E. of regression 15.49475 Akaike info criterion 8.371882

Sum squared resid 12484.55 Schwarz criterion 8.481373

Log likelihood -227.2267 Hannan-Quinn criter. 8.414223

F-statistic 752.0425 Durbin-Watson stat 1.981012

Prob(F-statistic) 0.000000 Inverted AR Roots 1.00

Inverted MA Roots -.42

IMPORT = 10172.921426 + [AR(1)=0.999512227566,MA(1)=0.418568245254,BACKCAST=1962,ESTSMPL="1962 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:30

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 11 iterations

MA Backcast: 1962 Variable Coefficient Std. Error t-Statistic Prob. C 5.018986 3.012170 1.666236 0.1018

AR(1) 0.002935 0.337055 0.008709 0.9931

MA(1) 0.416185 0.306080 1.359724 0.1799 R-squared 0.146932 Mean dependent var 4.920148

Adjusted R-squared 0.113479 S.D. dependent var 16.60856

S.E. of regression 15.63783 Akaike info criterion 8.391216

Sum squared resid 12471.63 Schwarz criterion 8.501715

Log likelihood -223.5628 Hannan-Quinn criter. 8.433831

F-statistic 4.392117 Durbin-Watson stat 1.984200

Prob(F-statistic) 0.017381 Inverted AR Roots .00

Inverted MA Roots -.42

D(IMPORT) = 5.01898583185 + [AR(1)=0.00293546671105,MA(1)=0.416184530896,BACKCAST=1963,ESTSMPL="1963 2016"]

ARMA (1.2)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:32

Sample (adjusted): 1962 2016

Included observations: 55 after adjustments

Convergence achieved after 82 iterations

MA Backcast: 1960 1961 Variable Coefficient Std. Error t-Statistic Prob. C -3.749411 8.570513 -0.437478 0.6636

AR(1) 1.069209 0.007633 140.0775 0.0000

MA(1) -0.247924 0.101732 -2.437034 0.0183

MA(2) -0.688092 0.099890 -6.888481 0.0000 R-squared 0.969393 Mean dependent var 78.76487

Adjusted R-squared 0.967593 S.D. dependent var 83.17724

S.E. of regression 14.97351 Akaike info criterion 8.320389

Sum squared resid 11434.50 Schwarz criterion 8.466377

Log likelihood -224.8107 Hannan-Quinn criter. 8.376844

F-statistic 538.4364 Durbin-Watson stat 1.481605

Prob(F-statistic) 0.000000 Inverted AR Roots 1.07

Estimated AR process is nonstationary

Inverted MA Roots .96 -.71

IMPORT = -3.74941133215 + [AR(1)=1.06920916796,MA(1)=-0.24792357854,MA(2)=-0.688092197864,BACKCAST=1962,ESTSMPL="1962 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:33

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 31 iterations

MA Backcast: 1961 1962

Variable Coefficient Std. Error t-Statistic Prob. C 6.563336 2.005507 3.272657 0.0019

AR(1) 0.870123 0.090241 9.642205 0.0000

MA(1) -0.537569 0.142378 -3.775660 0.0004

MA(2) -0.424089 0.132801 -3.193425 0.0024 R-squared 0.199819 Mean dependent var 4.920148

Adjusted R-squared 0.151808 S.D. dependent var 16.60856

S.E. of regression 15.29604 Akaike info criterion 8.364252

Sum squared resid 11698.44 Schwarz criterion 8.511584

Log likelihood -221.8348 Hannan-Quinn criter. 8.421072

F-statistic 4.161943 Durbin-Watson stat 1.943682

Prob(F-statistic) 0.010427 Inverted AR Roots .87

Inverted MA Roots .97 -.44

D(IMPORT) = 6.56333574834 + [AR(1)=0.870123079824,MA(1)=-0.537569117305,MA(2)=-0.424089148629,BACKCAST=1963,ESTSMPL="1963 2016"]

ARMA (1.3)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:38

Sample (adjusted): 1962 2016

Included observations: 55 after adjustments

Convergence achieved after 200 iterations

MA Backcast: 1959 1961 Variable Coefficient Std. Error t-Statistic Prob. C 45455.07 18821536 0.002415 0.9981

AR(1) 0.999885 0.047671 20.97471 0.0000

MA(1) 0.539987 0.185681 2.908146 0.0054

MA(2) 0.063585 0.229353 0.277235 0.7827

MA(3) -0.634339 0.176670 -3.590527 0.0008 R-squared 0.971832 Mean dependent var 78.76487

Adjusted R-squared 0.969579 S.D. dependent var 83.17724

S.E. of regression 14.50745 Akaike info criterion 8.273709

Sum squared resid 10523.30 Schwarz criterion 8.456194

Log likelihood -222.5270 Hannan-Quinn criter. 8.344278

F-statistic 431.2729 Durbin-Watson stat 2.175590

Prob(F-statistic) 0.000000 Inverted AR Roots 1.00

Inverted MA Roots .69 -.62+.73i -.62-.73i

IMPORT = 45455.0702175 + [AR(1)=0.999885068479,MA(1)=0.539986727663,MA(2)=0.0635849129352,MA(3)=-0.634339339274,BACKCAST=1962,ESTSMPL="1962 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:39

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 29 iterations

MA Backcast: 1960 1962 Variable Coefficient Std. Error t-Statistic Prob. C 5.285396 2.013597 2.624853 0.0115

AR(1) -0.159887 0.207067 -0.772152 0.4437

MA(1) 0.608544 0.174079 3.495783 0.0010

MA(2) 0.127426 0.196367 0.648919 0.5194

MA(3) -0.580257 0.148533 -3.906584 0.0003 R-squared 0.290502 Mean dependent var 4.920148

Adjusted R-squared 0.232583 S.D. dependent var 16.60856

S.E. of regression 14.54948 Akaike info criterion 8.281009

Sum squared resid 10372.68 Schwarz criterion 8.465174

Log likelihood -218.5872 Hannan-Quinn criter. 8.352034

F-statistic 5.015722 Durbin-Watson stat 2.027252

Prob(F-statistic) 0.001810 Inverted AR Roots -.16

Inverted MA Roots .63 -.62+.73i -.62-.73i

D(IMPORT) = 5.28539597861 + [AR(1)=-0.159887045754,MA(1)=0.608543712904,MA(2)=0.127425986916,MA(3)=-0.58025741824,BACKCAST=1963,ESTSMPL="1963 2016"]

ARMA (2.1)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:41

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 13 iterations

MA Backcast: 1962 Variable Coefficient Std. Error t-Statistic Prob. C -326.2629 1273.089 -0.256277 0.7988

AR(1) 0.995454 0.350266 2.841994 0.0065

AR(2) 0.017218 0.361645 0.047610 0.9622

MA(1) 0.423231 0.318384 1.329311 0.1898 R-squared 0.966156 Mean dependent var 80.16848

Adjusted R-squared 0.964125 S.D. dependent var 83.29819

S.E. of regression 15.77729 Akaike info criterion 8.426207

Sum squared resid 12446.14 Schwarz criterion 8.573539

Log likelihood -223.5076 Hannan-Quinn criter. 8.483027

F-statistic 475.7822 Durbin-Watson stat 1.994112

Prob(F-statistic) 0.000000 Inverted AR Roots 1.01 -.02

Estimated AR process is nonstationary

Inverted MA Roots -.42

IMPORT = -326.262853447 + [AR(1)=0.995454093565,AR(2)=0.0172179445643,MA(1)=0.423231185655,BACKCAST=1963,ESTSMPL="1963 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:40

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 13 iterations

MA Backcast: 1963 Variable Coefficient Std. Error t-Statistic Prob. C 5.302045 1.830711 2.896167 0.0056

AR(1) 0.613269 0.282913 2.167691 0.0351

AR(2) -0.501355 0.144908 -3.459823 0.0011

MA(1) -0.207926 0.317523 -0.654839 0.5156 R-squared 0.261368 Mean dependent var 5.008660

Adjusted R-squared 0.216145 S.D. dependent var 16.75463

S.E. of regression 14.83381 Akaike info criterion 8.304167

Sum squared resid 10782.05 Schwarz criterion 8.452868

Log likelihood -216.0604 Hannan-Quinn criter. 8.361350

F-statistic 5.779605 Durbin-Watson stat 2.057098

Prob(F-statistic) 0.001824 Inverted AR Roots .31+.64i .31-.64i

Inverted MA Roots .21

D(IMPORT) = 5.30204497347 + [AR(1)=0.613268638022,AR(2)=-0.501355471343,MA(1)=-0.207926342963,BACKCAST=1964,ESTSMPL="1964 2016"]

ARMA (2.2)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:43

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 143 iterations

MA Backcast: 1961 1962 Variable Coefficient Std. Error t-Statistic Prob. C 7424.894 472311.2 0.015720 0.9875

AR(1) 0.577134 0.555210 1.039488 0.3037

AR(2) 0.421872 0.559223 0.754390 0.4542

MA(1) 0.960971 0.512858 1.873757 0.0669

MA(2) 0.409950 0.217662 1.883426 0.0656 R-squared 0.967067 Mean dependent var 80.16848

Adjusted R-squared 0.964378 S.D. dependent var 83.29819

S.E. of regression 15.72148 Akaike info criterion 8.435954

Sum squared resid 12111.08 Schwarz criterion 8.620119

Log likelihood -222.7708 Hannan-Quinn criter. 8.506979

F-statistic 359.7134 Durbin-Watson stat 2.103569

Prob(F-statistic) 0.000000 Inverted AR Roots 1.00 -.42

Inverted MA Roots -.48-.42i -.48+.42i

IMPORT = 7424.89426989 + [AR(1)=0.577133946565,AR(2)=0.421872139106,MA(1)=0.960970638855,MA(2)=0.409950222562,BACKCAST=1963,ESTSMPL="1963 2016"]

Modelo corregido

Dependent Variable: D(IMPORT,2)

Method: Least Squares

Date: 09/29/17 Time: 20:44

Sample (adjusted): 1965 2016

Included observations: 52 after adjustments

Convergence achieved after 52 iterations

MA Backcast: OFF (Roots of MA process too large) Variable Coefficient Std. Error t-Statistic Prob. C 0.060843 0.053496 1.137353 0.2612

AR(1) -0.034060 0.427161 -0.079736 0.9368

AR(2) -0.245035 0.218549 -1.121187 0.2679

MA(1) -0.940072 0.388374 -2.420537 0.0194

MA(2) -0.475976 0.584153 -0.814815 0.4193 R-squared 0.605734 Mean dependent var 0.292173

Adjusted R-squared 0.572180 S.D. dependent var 20.01517

S.E. of regression 13.09152 Akaike info criterion 8.073017

Sum squared resid 8055.226 Schwarz criterion 8.260637

Log likelihood -204.8985 Hannan-Quinn criter. 8.144946

F-statistic 18.05223 Durbin-Watson stat 2.198900

Prob(F-statistic) 0.000000 Inverted AR Roots -.02-.49i -.02+.49i

Inverted MA Roots 1.30 -.36

Estimated MA process is noninvertible

D(IMPORT,2) = 0.0608434308167 + [AR(1)=-0.0340599128312,AR(2)=-0.245034546606,MA(1)=-0.940072378078,MA(2)=-0.475976448779,INITMA=1965,ESTSMPL="1965 2016"]

ARMA (2.3)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:47

Sample (adjusted): 1963 2016

Included observations: 54 after adjustments

Convergence achieved after 70 iterations

MA Backcast: OFF (Roots of MA process too large) Variable Coefficient Std. Error t-Statistic Prob. C -3.846372 3.348970 -1.148524 0.2564

AR(1) 0.992760 0.158389 6.267852 0.0000

AR(2) 0.073081 0.170123 0.429576 0.6694

MA(1) 0.076600 0.181109 0.422953 0.6742

MA(2) -0.674973 0.233218 -2.894177 0.0057

MA(3) -1.321151 0.189063 -6.987873 0.0000 R-squared 0.985246 Mean dependent var 80.16848

Adjusted R-squared 0.983709 S.D. dependent var 83.29819

S.E. of regression 10.63182 Akaike info criterion 7.670018

Sum squared resid 5425.705 Schwarz criterion 7.891017

Log likelihood -201.0905 Hannan-Quinn criter. 7.755249

F-statistic 641.0719 Durbin-Watson stat 2.372772

Prob(F-statistic) 0.000000 Inverted AR Roots 1.06 -.07

Estimated AR process is nonstationary

Inverted MA Roots 1.27 -.67-.76i -.67+.76i

Estimated MA process is noninvertible

IMPORT = -3.84637179178 + [AR(1)=0.992759527333,AR(2)=0.07308084102,MA(1)=0.0766004573245,MA(2)=-0.674973398822,MA(3)=-1.32115123969,INITMA=1963,ESTSMPL="1963 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 20:46

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 20 iterations

MA Backcast: 1961 1963

Variable Coefficient Std. Error t-Statistic Prob. C 5.508498 1.975182 2.788856 0.0076

AR(1) 0.251409 0.176663 1.423100 0.1613

AR(2) -0.671568 0.124183 -5.407896 0.0000

MA(1) 0.253290 0.203241 1.246254 0.2188

MA(2) 0.696163 0.142291 4.892542 0.0000

MA(3) -0.369341 0.193727 -1.906503 0.0627 R-squared 0.466634 Mean dependent var 5.008660

Adjusted R-squared 0.409892 S.D. dependent var 16.75463

S.E. of regression 12.87065 Akaike info criterion 8.054047

Sum squared resid 7785.718 Schwarz criterion 8.277099

Log likelihood -207.4322 Hannan-Quinn criter. 8.139822

F-statistic 8.223906 Durbin-Watson stat 2.063969

Prob(F-statistic) 0.000012 Inverted AR Roots .13-.81i .13+.81i

Inverted MA Roots .39 -.32-.92i -.32+.92i

D(IMPORT) = 5.50849758369 + [AR(1)=0.251408790351,AR(2)=-0.671568347491,MA(1)=0.253289526839,MA(2)=0.696162571011,MA(3)=-0.369340965925,BACKCAST=1964,ESTSMPL="1964 2016"]

ARMA (3.1)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 20:59

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 371 iterations

MA Backcast: 1963 Variable Coefficient Std. Error t-Statistic Prob. C 68681.93 42785481 0.001605 0.9987

AR(1) 1.613620 0.456778 3.532614 0.0009

AR(2) -1.114860 0.640964 -1.739350 0.0884

AR(3) 0.501172 0.246956 2.029397 0.0480

MA(1) -0.208063 0.540240 -0.385130 0.7018 R-squared 0.970184 Mean dependent var 81.62074

Adjusted R-squared 0.967699 S.D. dependent var 83.40231

S.E. of regression 14.98942 Akaike info criterion 8.342155

Sum squared resid 10784.77 Schwarz criterion 8.528031

Log likelihood -216.0671 Hannan-Quinn criter. 8.413634

F-statistic 390.4665 Durbin-Watson stat 2.056937

Prob(F-statistic) 0.000000 Inverted AR Roots 1.00 .31+.64i .31-.64i

Inverted MA Roots .21

IMPORT = 68681.9291712 + [AR(1)=1.61361990551,AR(2)=-1.11486039539,AR(3)=0.501171951081,MA(1)=-0.208062639668,BACKCAST=1964,ESTSMPL="1964 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 21:00

Sample (adjusted): 1965 2016

Included observations: 52 after adjustments

Convergence achieved after 14 iterations

MA Backcast: 1964 Variable Coefficient Std. Error t-Statistic Prob. C 5.384008 1.719422 3.131289 0.0030

AR(1) 0.000179 0.451181 0.000398 0.9997

AR(2) -0.187517 0.224827 -0.834048 0.4085

AR(3) -0.432174 0.196515 -2.199185 0.0328

MA(1) 0.366196 0.484574 0.755709 0.4536 R-squared 0.302204 Mean dependent var 5.098154

Adjusted R-squared 0.242817 S.D. dependent var 16.90530

S.E. of regression 14.71036 Akaike info criterion 8.306193

Sum squared resid 10170.55 Schwarz criterion 8.493812

Log likelihood -210.9610 Hannan-Quinn criter. 8.378122

F-statistic 5.088725 Durbin-Watson stat 1.910693

Prob(F-statistic) 0.001723 Inverted AR Roots .34-.73i .34+.73i -.67

Inverted MA Roots -.37

D(IMPORT) = 5.38400839857 + [AR(1)=0.00017949286528,AR(2)=-0.187516849583,AR(3)=-0.432173801713,MA(1)=0.366196457579,BACKCAST=1965,ESTSMPL="1965 2016"]

ARMA (3.2)

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 21:00

Sample (adjusted): 1965 2016

Included observations: 52 after adjustments

Convergence achieved after 23 iterations

MA Backcast: 1963 1964 Variable Coefficient Std. Error t-Statistic Prob. C 5.749701 2.164867 2.655914 0.0108

AR(1) -0.142165 0.105579 -1.346529 0.1847

AR(2) -0.703958 0.095836 -7.345427 0.0000

AR(3) -0.282056 0.168683 -1.672106 0.1013

MA(1) 0.631471 0.082306 7.672266 0.0000

MA(2) 0.999972 0.075141 13.30797 0.0000 R-squared 0.480762 Mean dependent var 5.098154

Adjusted R-squared 0.424323 S.D. dependent var 16.90530

S.E. of regression 12.82663 Akaike info criterion 8.049090

Sum squared resid 7568.027 Schwarz criterion 8.274234

Log likelihood -203.2763 Hannan-Quinn criter. 8.135405

F-statistic 8.518255 Durbin-Watson stat 2.037114

Prob(F-statistic) 0.000009 Inverted AR Roots .11+.88i .11-.88i -.36

Inverted MA Roots -.32+.95i -.32-.95i

D(IMPORT) = 5.74970117731 + [AR(1)=-0.142165264007,AR(2)=-0.703957842492,AR(3)=-0.28205596446,MA(1)=0.631471330392,MA(2)=0.999971602493,BACKCAST=1965,ESTSMPL="1965 2016"]

Modelo corregido

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 21:02

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 21 iterations

MA Backcast: 1962 1963 Variable Coefficient Std. Error t-Statistic Prob. C 1210.647 5311.602 0.227925 0.8207

AR(1) 1.001022 0.071582 13.98428 0.0000

AR(2) -0.769637 0.109726 -7.014183 0.0000

AR(3) 0.759176 0.077512 9.794303 0.0000

MA(1) 0.562415 0.062218 9.039486 0.0000

MA(2) 0.999933 0.076127 13.13497 0.0000 R-squared 0.977504 Mean dependent var 81.62074

Adjusted R-squared 0.975111 S.D. dependent var 83.40231

S.E. of regression 13.15767 Akaike info criterion 8.098157

Sum squared resid 8136.839 Schwarz criterion 8.321209

Log likelihood -208.6012 Hannan-Quinn criter. 8.183932

F-statistic 408.4607 Durbin-Watson stat 2.138404

Prob(F-statistic) 0.000000 Inverted AR Roots .99 .00+.87i .00-.87i

Inverted MA Roots -.28+.96i -.28-.96i

IMPORT = 1210.64700668 + [AR(1)=1.00102176072,AR(2)=-0.769636933817,AR(3)=0.759175887777,MA(1)=0.562414547523,MA(2)=0.999932504406,BACKCAST=1964,ESTSMPL="1964 2016"]

ARMA (3.3)

Dependent Variable: IMPORT

Method: Least Squares

Date: 09/29/17 Time: 21:03

Sample (adjusted): 1964 2016

Included observations: 53 after adjustments

Convergence achieved after 64 iterations

MA Backcast: OFF (Roots of MA process too large)

Variable Coefficient Std. Error t-Statistic Prob. C -3.898700 2.869286 -1.358770 0.1808

AR(1) 1.160229 0.271330 4.276075 0.0001

AR(2) -0.285963 0.474135 -0.603125 0.5494

AR(3) 0.198134 0.277512 0.713963 0.4789

MA(1) -0.332516 0.255108 -1.303433 0.1989

MA(2) -0.435287 0.314045 -1.386065 0.1724

MA(3) -0.959882 0.239570 -4.006686 0.0002 R-squared 0.985072 Mean dependent var 81.62074

Adjusted R-squared 0.983125 S.D. dependent var 83.40231

S.E. of regression 10.83441 Akaike info criterion 7.725831

Sum squared resid 5399.682 Schwarz criterion 7.986059

Log likelihood -197.7345 Hannan-Quinn criter. 7.825902

F-statistic 505.9012 Durbin-Watson stat 2.070780

Prob(F-statistic) 0.000000 Inverted AR Roots 1.07 .05+.43i .05-.43i

Estimated AR process is nonstationary

Inverted MA Roots 1.27 -.47-.73i -.47+.73i

Estimated MA process is noninvertible

IMPORT = -3.89870004389 + [AR(1)=1.16022921141,AR(2)=-0.285962555425,AR(3)=0.19813373858,MA(1)=-0.332516485683,MA(2)=-0.43528658266,MA(3)=-0.959881847931,INITMA=1964,ESTSMPL="1964 2016"]

Modelo corregido

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 21:04

Sample (adjusted): 1965 2016

Included observations: 52 after adjustments

Convergence achieved after 25 iterations

MA Backcast: 1962 1964 Variable Coefficient Std. Error t-Statistic Prob. C 6.938916 2.104094 3.297816 0.0019

AR(1) 0.946188 0.125358 7.547875 0.0000

AR(2) -0.783347 0.165160 -4.742950 0.0000

AR(3) 0.632305 0.135977 4.650075 0.0000

MA(1) -0.409844 0.066933 -6.123168 0.0000

MA(2) 0.382045 0.068454 5.581046 0.0000

MA(3) -0.911084 0.047298 -19.26263 0.0000 R-squared 0.460080 Mean dependent var 5.098154

Adjusted R-squared 0.388091 S.D. dependent var 16.90530

S.E. of regression 13.22410 Akaike info criterion 8.126609

Sum squared resid 7869.463 Schwarz criterion 8.389277

Log likelihood -204.2918 Hannan-Quinn criter. 8.227310

F-statistic 6.390952 Durbin-Watson stat 2.247087

Prob(F-statistic) 0.000064 Inverted AR Roots .88 .04+.85i .04-.85i

Inverted MA Roots .98 -.28+.92i -.28-.92i

D(IMPORT) = 6.93891587165 + [AR(1)=0.94618803211,AR(2)=-0.783346580642,AR(3)=0.632304667344,MA(1)=-0.409844163596,MA(2)=0.382045440611,MA(3)=-0.911083737684,BACKCAST=1965,ESTSMPL="1965 2016"]

TEST DE LA RAIZ UNITARIA PARA DETECTAR SI EL MODELO DE

IMPORTACIONES KEYNESIANO ES NO ESTACIONARIO

Null Hypothesis: IMPORT has a unit root

Exogenous: Constant

Lag Length: 3 (Automatic - based on SIC, maxlag=10) t-Statistic Prob.* Augmented Dickey-Fuller test statistic 4.296239 1.0000

Test critical values: 1% level -3.562669

5% level -2.918778

10% level -2.597285 *MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(IMPORT)

Method: Least Squares

Date: 09/29/17 Time: 21:07

Sample (adjusted): 1965 2016

Included observations: 52 after adjustments Variable Coefficient Std. Error t-Statistic Prob. IMPORT(-1) 0.151053 0.035159 4.296239 0.0001

D(IMPORT(-1)) 0.040430 0.141032 0.286674 0.7756

D(IMPORT(-2)) -0.446245 0.125565 -3.553890 0.0009

D(IMPORT(-3)) -0.800826 0.187835 -4.263459 0.0001

C 0.369330 2.514581 0.146875 0.8839 R-squared 0.484590 Mean dependent var 5.098154

Adjusted R-squared 0.440726 S.D. dependent var 16.90530

S.E. of regression 12.64257 Akaike info criterion 8.003228

Sum squared resid 7512.222 Schwarz criterion 8.190847

Log likelihood -203.0839 Hannan-Quinn criter. 8.075157

F-statistic 11.04740 Durbin-Watson stat 2.135721

Prob(F-statistic) 0.000002

Null Hypothesis: D(IMPORT,2) has a unit root

Exogenous: Constant

Lag Length: 5 (Automatic - based on SIC, maxlag=10) t-Statistic Prob.* Augmented Dickey-Fuller test statistic -5.610517 0.0000

Test critical values: 1% level -3.574446

5% level -2.923780

10% level -2.599925 *MacKinnon (1996) one-sided p-values.

Augmented Dickey-Fuller Test Equation

Dependent Variable: D(IMPORT,3)

Method: Least Squares

Date: 09/29/17 Time: 21:05

Sample (adjusted): 1969 2016

Included observations: 48 after adjustments Variable Coefficient Std. Error t-Statistic Prob. D(IMPORT(-1),2) -6.275841 1.118585 -5.610517 0.0000

D(IMPORT(-1),3) 4.595988 1.033976 4.444964 0.0001

D(IMPORT(-2),3) 3.790901 0.882640 4.294957 0.0001

D(IMPORT(-3),3) 2.195984 0.695473 3.157540 0.0030

D(IMPORT(-4),3) 1.049417 0.500094 2.098437 0.0421

D(IMPORT(-5),3) 0.736856 0.260274 2.831080 0.0072

C 2.677244 1.884219 1.420877 0.1629 R-squared 0.854581 Mean dependent var 0.791333

Adjusted R-squared 0.833300 S.D. dependent var 30.08883

S.E. of regression 12.28494 Akaike info criterion 7.988663

Sum squared resid 6187.710 Schwarz criterion 8.261547

Log likelihood -184.7279 Hannan-Quinn criter. 8.091786

F-statistic 40.15727 Durbin-Watson stat 2.086898

Prob(F-statistic) 0.000000