View
6
Download
0
Category
Preview:
Citation preview
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
Recommended