Apresentam-se abaixo as análises dos modelos mais adequados a cada uma das séries estudadas. Optamos por separar estas análises por serem muito extensas, mitigando assim qualquer problema apresentação do trabalho.
EGARCH(1,1,1)
Dependent Variable: RET_ALEMANHA ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 1.069979 Probability 0.382550
Obs*R-squared 10.70298 Probability 0.381122 Sample (adjusted): 7 1022 Test Equation: Included observations: 1016 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 24 iterations Method: Least Squares MA backcast: 2 6, Variance backcast: ON LOG(GARCH) = C(8) + C(9)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + Sample (adjusted): 17 1022 C(10)*RESID(-1)/@SQRT(GARCH(-1)) + C(11)*LOG(GARCH(-1)) Included observations: 1006 after adjustments
Coefficient Std.
Error z-Statistic Prob. Variable Coefficient Std. Error t-Statistic Prob. AR(1) -0.020186 0.009548 -2.114310 0.0345 C 0.970448 0.115134 8.428851 0.0000 AR(2) 0.023699 0.010421 2.274233 0.0230 STD_RESID^2(-1) -0.051754 0.031650 -1.635191 0.1023 AR(3) 0.035801 0.016234 2.205366 0.0274 STD_RESID^2(-2) -0.002283 0.031687 -0.072045 0.9426 AR(5) -0.937041 0.016413 -57.08990 0.0000 STD_RESID^2(-3) 0.052714 0.031682 1.663828 0.0965 MA(3) -0.047574 0.015801 -3.010814 0.0026 STD_RESID^2(-4) 0.024833 0.031928 0.777763 0.4369 MA(4) -0.027462 0.010047 -2.733410 0.0063 STD_RESID^2(-5) -0.010386 0.031937 -0.325188 0.7451 MA(5) 0.940601 0.016817 55.93256 0.0000 STD_RESID^2(-6) -0.011811 0.031937 -0.369813 0.7116 Variance Equation STD_RESID^2(-7) 0.012142 0.031952 0.380009 0.7040 C(8) -0.284483 0.039552 -7.192714 0.0000 STD_RESID^2(-8) -0.018082 0.031920 -0.566477 0.5712 C(9) 0.123534 0.026256 4.705039 0.0000 STD_RESID^2(-9) -0.019627 0.031925 -0.614777 0.5388
C(10) -0.135228 0.011739 -11.51934 0.0000
STD_RESID^2(-
10) 0.057114 0.031898 1.790536 0.0737 C(11) 0.978030 0.003238 302.0332 0.0000 R-squared 0.010639 Mean dependent var 1.003130
R-squared 0.025131 Mean dependent var 4.17E-05
Adjusted R-
squared 0.000696 S.D. dependent var 1.743570 Adjusted R-squared 0.015431 S.D. dependent var 0.016357 S.E. of regression 1.742963 Akaike info criterion 3.959925 S.E. of regression 0.016230 Akaike info criterion -5.876604 Sum squared resid 3022.732 Schwarz criterion 4.013654
Sum squared resid 0.264738 Schwarz criterion -5.823297 Log likelihood -1980.842 F-
statistic 1.069979
Log likelihood 2996.315 Durbin-Watson stat 2.034873
Durbin-Watson
stat 2.006837 Prob(F-statistic) 0.382550
Inverted AR Roots .80+.57i .80-
.57i -.32-.94i -.32+.94i
-.99
Inverted MA Roots .80+.57i .80-
.57i -.31-.95i -.31+.95i
-.98
Tabela 13 - Série de Volatilidade EGARCH(1,1,1) da Alemanha Tabela 14 - Teste LM dos Resíduos EGARCH(1,1,1) da Alemanha
80
Dependent Variable: RET_AUSTRALIA ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 0.530651 Probability 0.869267
Obs*R-squared 5.336649 Probability 0.867586 Sample (adjusted): 5 1022 Test Equation: Included observations: 1018 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 22 iterations Method: Least Squares MA backcast: 1 4, Variance backcast: ON LOG(GARCH) = C(6) + C(7)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + Sample (adjusted): 15 1022 C(8)*RESID(-1)/@SQRT(GARCH(-1)) + C(9)*LOG(GARCH(-1)) Included observations: 1008 after adjustments Coefficient Std. Error z-Statistic Prob. Variable Coefficient Std. Error t-Statistic Prob. AR(1) -0.070539 0.017345 -4.066808 0.0000 C 0.905950 0.108618 8.340668 0.0000 AR(2) 0.035878 0.011342 3.163362 0.0016 STD_RESID^2(-1) -0.029681 0.031672 -0.937131 0.3489 AR(3) 0.928490 0.017921 51.80893 0.0000 STD_RESID^2(-2) -0.011292 0.031657 -0.356710 0.7214 MA(3) -0.914981 0.016519 -55.38865 0.0000 STD_RESID^2(-3) 0.040764 0.031874 1.278887 0.2012 MA(4) 0.095432 0.013402 7.120892 0.0000 STD_RESID^2(-4) 0.042837 0.031900 1.342863 0.1796 Variance Equation STD_RESID^2(-5) 0.013246 0.031932 0.414837 0.6784 C(6) -0.275175 0.056633 -4.858886 0.0000 STD_RESID^2(-6) 0.005164 0.031938 0.161699 0.8716 C(7) 0.110158 0.027498 4.006073 0.0001 STD_RESID^2(-7) 0.001303 0.031906 0.040835 0.9674 C(8) -0.144154 0.014885 -9.684233 0.0000 STD_RESID^2(-8) 0.026729 0.031875 0.838560 0.4019 C(9) 0.978948 0.004962 197.3059 0.0000 STD_RESID^2(-9) 6.78E-05 0.031885 0.002126 0.9983
R-squared -0.000533 Mean dependent var -5.13E-06
STD_RESID^2(-
10) 0.004444 0.031869 0.139459 0.8891 Adjusted R-squared -0.008466 S.D. dependent var 0.013814 R-squared 0.005294 Mean dependent var 0.998763
S.E. of regression 0.013873 Akaike info criterion -6.123559
Adjusted R-
squared -0.004683 S.D. dependent var 1.571536 Sum squared resid 0.194183 Schwarz criterion -6.080013 S.E. of regression 1.575211 Akaike info criterion 3.757508 Log likelihood 3125.892 Durbin-Watson stat 1.908854 Sum squared resid 2473.846 Schwarz criterion 3.811152
Inverted AR Roots .96 -
.52+.83i -.52-.83i Log likelihood -1882.784 F-
statistic 0.530651
Inverted MA Roots .93 .10 -.52+.84i -.52-.84i
Durbin-Watson
stat 1.999849 Prob(F-statistic) 0.869267
Tabela 15 - Série de Volatilidade EGARCH(1,1,1) da Austrália Tabela 16 - Teste LM dos Resíduos EGARCH(1,1,1) da Austrália
81
Dependent Variable: RET_CHINA ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 0.679367 Probability 0.744390
Obs*R-squared 6.822171 Probability 0.742120 Sample (adjusted): 6 1022 Test Equation: Included observations: 1017 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 30 iterations Method: Least Squares MA backcast: 2 5, Variance backcast: ON LOG(GARCH) = C(7) + C(8)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + Sample (adjusted): 16 1022 C(9)*RESID(-1)/@SQRT(GARCH(-1)) + C(10)*LOG(GARCH(-1)) Included observations: 1007 after adjustments
Coefficient Std.
Error z-Statistic Prob. Variable Coefficient Std. Error t-Statistic Prob. AR(1) 1.085412 0.021498 50.48964 0.0000 C 0.995241 0.116187 8.565883 0.0000 AR(3) -0.978983 0.049133 -19.92530 0.0000 STD_RESID^2(-1) 0.027008 0.031664 0.852950 0.3939 AR(4) 0.887281 0.038039 23.32559 0.0000 STD_RESID^2(-2) -0.007773 0.031652 -0.245580 0.8061 MA(1) -1.093210 0.015961 -68.49404 0.0000 STD_RESID^2(-3) 0.031886 0.031630 1.008074 0.3137 MA(3) 1.041756 0.036202 28.77605 0.0000 STD_RESID^2(-4) 0.014046 0.031711 0.442944 0.6579 MA(4) -0.916832 0.030589 -29.97284 0.0000 STD_RESID^2(-5) -0.009537 0.031705 -0.300795 0.7636 Variance Equation STD_RESID^2(-6) 0.001353 0.031899 0.042400 0.9662 C(7) -0.306255 0.047186 -6.490434 0.0000 STD_RESID^2(-7) -0.011439 0.031900 -0.358593 0.7200 C(8) 0.154398 0.018450 8.368652 0.0000 STD_RESID^2(-8) -0.038273 0.031881 -1.200512 0.2302 C(9) -0.039358 0.013479 -2.919958 0.0035 STD_RESID^2(-9) -0.041416 0.031905 -1.298126 0.1945 C(10) 0.975114 0.005622 173.4438 0.0000 STD_RESID^2(- 10) 0.036772 0.031920 1.152010 0.2496 R-squared 0.007231 Mean dependent var 0.000965 R-squared 0.006775 Mean dependent var 0.998352
Adjusted R-squared -0.001642 S.D. dependent var 0.021219
Adjusted R-
squared -0.003197 S.D. dependent var 2.029192 S.E. of regression 0.021237 Akaike info criterion -5.022441 S.E. of regression 2.032433 Akaike info criterion 4.267208 Sum squared resid 0.454160 Schwarz criterion -4.974019 Sum squared resid 4114.261 Schwarz criterion 4.320894
Log likelihood 2563.911 Durbin-Watson stat 2.013759 Log likelihood -2137.539 F- statistic 0.679367 Inverted AR Roots 1.00 .53+.80i .53-.80i -.96 Durbin-Watson stat 2.002549 Prob(F-statistic) 0.744390 Inverted MA Roots .98 .54- .81i .54+.81i -.98
Tabela 17 - Série de Volatilidade EGARCH(1,1,1) da China Tabela 18 - Teste LM dos Resíduos EGARCH(1,1,1) da China
82
Dependent Variable: RET_EUA ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 2.408963 Probability 0.007876
Obs*R-squared 23.78022 Probability 0.008206 Sample (adjusted): 7 1022 Test Equation: Included observations: 1016 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 46 iterations Method: Least Squares MA backcast: 2 6, Variance backcast: ON LOG(GARCH) = C(7) + C(8)*ABS(RESID(-1)/@SQRT(GARCH(-1))) + Sample (adjusted): 17 1022 C(9)*RESID(-1)/@SQRT(GARCH(-1)) + C(10)*LOG(GARCH(-1)) Included observations: 1006 after adjustments
Coefficient Std.
Error z-Statistic Prob. Variable Coefficient Std. Error t-Statistic Prob. AR(1) -0.046127 0.005821 -7.923909 0.0000 C 0.815643 0.115972 7.033090 0.0000 AR(3) 0.947360 0.007769 121.9360 0.0000 STD_RESID^2(-1) -0.076964 0.031538 -2.440397 0.0148 AR(5) 0.081798 0.005237 15.62079 0.0000 STD_RESID^2(-2) -0.021180 0.031027 -0.682628 0.4950 MA(3) -0.957070 0.004998 -191.5025 0.0000 STD_RESID^2(-3) -0.010952 0.031035 -0.352888 0.7242 MA(4) 0.077178 0.004369 17.66679 0.0000 STD_RESID^2(-4) 0.058659 0.031039 1.889883 0.0591 MA(5) -0.050141 0.005843 -8.582003 0.0000 STD_RESID^2(-5) 0.036457 0.031094 1.172482 0.2413 Variance Equation STD_RESID^2(-6) 0.013255 0.031101 0.426200 0.6701 C(7) 0.000551 0.001084 0.507907 0.6115 STD_RESID^2(-7) 0.011757 0.031040 0.378772 0.7049 C(8) -0.031799 5.76E-05 -551.9475 0.0000 STD_RESID^2(-8) 0.031261 0.031042 1.007068 0.3141 C(9) -0.160949 0.012292 -13.09389 0.0000 STD_RESID^2(-9) 0.049313 0.031051 1.588128 0.1126 C(10) 0.997774 3.17E-06 314806.3 0.0000 STD_RESID^2(- 10) 0.100011 0.030987 3.227483 0.0013 R-squared 0.028181 Mean dependent var -0.000149 R-squared 0.023638 Mean dependent var 1.012374
Adjusted R-squared 0.019487 S.D. dependent var 0.016541
Adjusted R-
squared 0.013826 S.D. dependent var 1.813048 S.E. of regression 0.016379 Akaike info criterion -6.167242 S.E. of regression 1.800472 Akaike info criterion 4.024848 Sum squared resid 0.269876 Schwarz criterion -6.118781 Sum squared resid 3225.489 Schwarz criterion 4.078577
Log likelihood 3142.959 Durbin-Watson stat 2.173814 Log likelihood -2013.499 F-
statistic 2.408963
Inverted AR Roots .99
.00+.29i .00-.29i -.52+.83i
Durbin-Watson
stat 1.998715 Prob(F-statistic) 0.007876
-.52-.83i
Inverted MA Roots .98
.04+.22i .04-.22i -.53-.84i
-.53+.84i
Tabela 19 - Série de Volatilidade EGARCH(1,1,1) dos EUA Tabela 20 - Teste LM dos Resíduos EGARCH(1,1,1) dos EUA
83 TGARCH(1,1,1)
Dependent Variable: RET_BRASIL ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 1.055436 Probability 0.394384
Obs*R-squared 10.55903 Probability 0.392888 Sample (adjusted): 6 1022 Test Equation: Included observations: 1017 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 49 iterations Method: Least Squares MA backcast: 1 5, Variance backcast: ON GARCH = C(7) + C(8)*RESID(-1)^2 + C(9)*RESID(-1)^2*(RESID(-1)<0) Sample (adjusted): 16 1022 + C(10)*GARCH(-1) Included observations: 1007 after adjustments
Coefficient Std.
Error z-Statistic Prob. Variable Coefficient Std. Error t-Statistic Prob. AR(1) -0.031164 0.006800 -4.582790 0.0000 C 0.998545 0.118122 8.453504 0.0000 AR(2) 1.749139 0.012426 140.7668 0.0000 STD_RESID^2(-1) -0.057503 0.031621 -1.818518 0.0693 AR(4) -0.918258 0.010719 -85.66335 0.0000 STD_RESID^2(-2) 0.014274 0.031609 0.451565 0.6517 MA(2) -1.787040 0.005400 -330.9266 0.0000 STD_RESID^2(-3) 0.011703 0.031575 0.370648 0.7110 MA(4) 0.961670 0.009388 102.4340 0.0000 STD_RESID^2(-4) 0.003559 0.031577 0.112707 0.9103 MA(5) 0.015181 0.006182 2.455464 0.0141 STD_RESID^2(-5) -0.000344 0.031571 -0.010893 0.9913 Variance Equation STD_RESID^2(-6) 0.021392 0.031567 0.677654 0.4981 C 1.28E-05 2.59E-06 4.948848 0.0000 STD_RESID^2(-7) -0.004909 0.031576 -0.155463 0.8765 RESID(-1)^2 -0.005937 0.014650 -0.405279 0.6853 STD_RESID^2(-8) -0.049864 0.031572 -1.579397 0.1146 RESID(-1)^2*(RESID(- 1)<0) 0.166181 0.028857 5.758796 0.0000 STD_RESID^2(-9) -0.001850 0.031614 -0.058524 0.9533 GARCH(-1) 0.891736 0.018464 48.29670 0.0000 STD_RESID^2(- 10) 0.063292 0.031561 2.005365 0.0452 R-squared 0.029860 Mean dependent var 0.000646 R-squared 0.010486 Mean dependent var 0.998689
Adjusted R-squared 0.021189 S.D. dependent var 0.022066
Adjusted R-
squared 0.000551 S.D. dependent var 1.775922 S.E. of regression 0.021831 Akaike info criterion -5.163956 S.E. of regression 1.775433 Akaike info criterion 3.996829 Sum squared resid 0.479919 Schwarz criterion -5.115533 Sum squared resid 3139.553 Schwarz criterion 4.050515
Log likelihood 2635.872 Durbin-Watson stat 2.021318 Log likelihood -2001.403 F-
statistic 1.055436
Inverted AR Roots .95-.22i
.95+.22i -.97-.19i -.97+.19i
Durbin-Watson
stat 1.998990 Prob(F-statistic) 0.394384
Inverted MA Roots .97-.22i
.97+.22i -.02 -.96-.20i
-.96+.20i
Tabela 21 - Série de Volatilidade TGARCH(1,1,1) do Brasil Tabela 22 - Teste LM dos Resíduos TGARCH(1,1,1) do Brasil
84
Dependent Variable: RET_JAPAO ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 2.111237 Probability 0.021267
Obs*R-squared 20.90226 Probability 0.021786 Sample (adjusted): 7 1022 Test Equation: Included observations: 1016 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 18 iterations Method: Least Squares MA backcast: 2 6, Variance backcast: ON GARCH = C(5) + C(6)*RESID(-1)^2 + C(7)*RESID(-1)^2*(RESID(-1)<0) Sample (adjusted): 17 1022 + C(8)*GARCH(-1) Included observations: 1006 after adjustments
Coefficient Std.
Error z-Statistic Prob. Variable Coefficient Std. Error t-Statistic Prob. AR(1) -0.008647 0.006036 -1.432575 0.1520 C 1.001458 0.112441 8.906536 0.0000 AR(4) -0.009612 0.005562 -1.728256 0.0839 STD_RESID^2(-1) -0.090643 0.031712 -2.858364 0.0043 AR(5) 0.965904 0.007206 134.0354 0.0000 STD_RESID^2(-2) -0.007416 0.031755 -0.233526 0.8154 MA(5) -0.983022 0.003825 -256.9874 0.0000 STD_RESID^2(-3) 0.040540 0.032034 1.265522 0.2060 Variance Equation STD_RESID^2(-4) 0.057090 0.032041 1.781760 0.0751 C 3.69E-06 6.83E-07 5.403059 0.0000 STD_RESID^2(-5) 0.049449 0.032041 1.543296 0.1231 RESID(-1)^2 -0.037631 0.012897 -2.917859 0.0035 STD_RESID^2(-6) 0.020644 0.032038 0.644353 0.5195 RESID(-1)^2*(RESID(-
1)<0) 0.162352 0.018565 8.744942 0.0000 STD_RESID^2(-7) -0.000830 0.031993 -0.025949 0.9793 GARCH(-1) 0.929177 0.011087 83.80492 0.0000 STD_RESID^2(-8) 0.002699 0.031968 0.084437 0.9327 R-squared -0.001375 Mean dependent var -0.000532 STD_RESID^2(-9) -0.083901 0.031965 -2.624780 0.0088
Adjusted R-squared -0.008329 S.D. dependent var 0.018655
STD_RESID^2(-
10) 0.011361 0.031936 0.355741 0.7221 S.E. of regression 0.018733 Akaike info criterion -5.626233 R-squared 0.020778 Mean dependent var 0.999730
Sum squared resid 0.353730 Schwarz criterion -5.587464
Adjusted R-
squared 0.010936 S.D. dependent var 1.598065 Log likelihood 2866.126 Durbin-Watson stat 1.997338 S.E. of regression 1.589303 Akaike info criterion 3.775342
Inverted AR Roots .99
.31+.94i .31-.94i -.81-.59i Sum squared resid 2513.254 Schwarz criterion 3.829071
-.81+.59i Log likelihood -1887.997 F-
statistic 2.111237
Inverted MA Roots 1.00
.31-
.95i .31+.95i -.81-.59i
Durbin-Watson
stat 1.998407 Prob(F-statistic) 0.021267
-.81+.59i
Tabela 23 - Série de Volatilidade TGARCH(1,1,1) do Japão Tabela 24 - Teste LM dos Resíduos TGARCH(1,1,1) do Japão
85
Dependent Variable: RET_REINOUNIDO ARCH Test: Method: ML - ARCH (Marquardt) - Normal distribution F-statistic 1.059765 Probability 0.390840
Obs*R-squared 10.60189 Probability 0.389363 Sample (adjusted): 7 1022 Test Equation: Included observations: 1016 after adjustments Dependent Variable: STD_RESID^2 Convergence achieved after 33 iterations Method: Least Squares MA backcast: OFF (Roots of MA process too large), Variance backcast: ON Sample (adjusted): 17 1022 GARCH = C(9) + C(10)*RESID(-1)^2 + C(11)*RESID(-1)^2*(RESID( Included observations: 1006 after adjustments -1)<0) + C(12)*GARCH(-1) Variable Coefficient Std. Error t-Statistic Prob.
Coefficient Std.
Error z-Statistic Prob. C 1.069076 0.116364 9.187376 0.0000 AR(1) -0.058256 0.008658 -6.728637 0.0000 STD_RESID^2(-1) -0.040153 0.031691 -1.267029 0.2054 AR(2) -1.053435 0.012553 -83.92024 0.0000 STD_RESID^2(-2) -0.051509 0.031684 -1.625693 0.1043 AR(4) -0.767585 0.012107 -63.39874 0.0000 STD_RESID^2(-3) 0.043112 0.031722 1.359035 0.1744 AR(5) 0.369322 0.009297 39.72592 0.0000 STD_RESID^2(-4) 0.001712 0.032266 0.053055 0.9577 MA(2) 1.023868 0.011018 92.92995 0.0000 STD_RESID^2(-5) 0.008354 0.032237 0.259154 0.7956 MA(3) -0.093967 0.010132 -9.273859 0.0000 STD_RESID^2(-6) 0.037638 0.032230 1.167788 0.2432 MA(4) 0.751170 0.009285 80.90085 0.0000 STD_RESID^2(-7) -0.025731 0.032264 -0.797507 0.4253 MA(5) -0.454686 0.012962 -35.07781 0.0000 STD_RESID^2(-8) -0.011639 0.032250 -0.360903 0.7182 Variance Equation STD_RESID^2(-9) -0.044486 0.032212 -1.381049 0.1676
C 1.62E-06 3.58E-07 4.521339 0.0000
STD_RESID^2(-
10) 0.018848 0.032229 0.584815 0.5588 RESID(-1)^2 -0.000643 0.015093 -0.042597 0.9660 R-squared 0.010539 Mean dependent var 1.005385 RESID(-1)^2*(RESID(-
1)<0) 0.156096 0.021021 7.425661 0.0000
Adjusted R-
squared 0.000594 S.D. dependent var 1.601880 GARCH(-1) 0.915612 0.012263 74.66421 0.0000 S.E. of regression 1.601404 Akaike info criterion 3.790512 R-squared 0.036702 Mean dependent var -7.48E-05 Sum squared resid 2551.672 Schwarz criterion 3.844241
Adjusted R-squared 0.026148 S.D. dependent var 0.015405 Log likelihood -1895.628 F-
statistic 1.059765
S.E. of regression 0.015202 Akaike info criterion -6.091244
Durbin-Watson
stat 1.997360 Prob(F-statistic) 0.390840 Sum squared resid 0.232021 Schwarz criterion -6.033091 Log likelihood 3106.352 Durbin-Watson stat 2.062754
Inverted AR Roots .39
.33-
.94i .33+.94i -.55-.81i
-.55+.81i
Inverted MA Roots .47
.33-
.95i .33+.95i -.56+.81i
-.56-.81i
Estimated MA process is noninvertible
Tabela 25 - Série de Volatilidade TGARCH(1,1,1) do Reino Unido Tabela 26 - Teste LM dos Resíduos TGARCH(1,1,1) do Reino Unido
86