--------------------------------------------------------------------------------- . *Osa 1 GARCH mudeli hindamine . arch LRET, arch(1/1) arima(1,0,0) (setting optimization to BHHH) Iteration 0: Log likelihood = -3869.0044 Iteration 1: Log likelihood = -3864.3499 Iteration 2: Log likelihood = -3863.8355 Iteration 3: Log likelihood = -3863.7241 Iteration 4: Log likelihood = -3863.7055 (switching optimization to BFGS) Iteration 5: Log likelihood = -3863.6951 Iteration 6: Log likelihood = -3863.685 Iteration 7: Log likelihood = -3863.6778 Iteration 8: Log likelihood = -3863.674 Iteration 9: Log likelihood = -3863.6738 Iteration 10: Log likelihood = -3863.6738 ARCH family regression -- AR disturbances Sample: 1 thru 2518 Number of obs = 2518 Wald chi2(1) = 66.01 Log likelihood = -3863.674 Prob > chi2 = 0.0000 ------------------------------------------------------------------------------ | OPG LRET | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- LRET | _cons | .1151729 .0176626 6.52 0.000 .0805549 .149791 -------------+---------------------------------------------------------------- ARMA | ar | L1. | -.0990675 .0121938 -8.12 0.000 -.1229669 -.075168 -------------+---------------------------------------------------------------- ARCH | arch | L1. | .3836782 .025378 15.12 0.000 .3339382 .4334181 | _cons | .9299436 .0211958 43.87 0.000 .8884007 .9714865 ------------------------------------------------------------------------------ . estat ic Akaike's information criterion and Bayesian information criterion ----------------------------------------------------------------------------- Model | N ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 2,518 . -3863.674 4 7735.348 7758.672 ----------------------------------------------------------------------------- Note: BIC uses N = number of observations. See [R] IC note. . arch LRET, arch(1/1) garch(1/1) arima(1,0,0) (setting optimization to BHHH) Iteration 0: Log likelihood = -3706.2766 Iteration 1: Log likelihood = -3619.6382 Iteration 2: Log likelihood = -3580.1158 Iteration 3: Log likelihood = -3571.6851 Iteration 4: Log likelihood = -3571.2074 (switching optimization to BFGS) Iteration 5: Log likelihood = -3571.1761 Iteration 6: Log likelihood = -3571.1652 Iteration 7: Log likelihood = -3571.1652 Iteration 8: Log likelihood = -3571.1652 ARCH family regression -- AR disturbances Sample: 1 thru 2518 Number of obs = 2518 Wald chi2(1) = 3.81 Log likelihood = -3571.165 Prob > chi2 = 0.0511 ------------------------------------------------------------------------------ | OPG LRET | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- LRET | _cons | .0915546 .0164507 5.57 0.000 .0593119 .1237974 -------------+---------------------------------------------------------------- ARMA | ar | L1. | -.041704 .0213751 -1.95 0.051 -.0835985 .0001905 -------------+---------------------------------------------------------------- ARCH | arch | L1. | .1565655 .013794 11.35 0.000 .1295296 .1836013 | garch | L1. | .7992056 .0166879 47.89 0.000 .766498 .8319132 | _cons | .0592067 .0072532 8.16 0.000 .0449907 .0734226 ------------------------------------------------------------------------------ . estat ic Akaike's information criterion and Bayesian information criterion ----------------------------------------------------------------------------- Model | N ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 2,518 . -3571.165 5 7152.33 7181.487 ----------------------------------------------------------------------------- Note: BIC uses N = number of observations. See [R] IC note. . arch LRET, arch(1/2) garch(1/1) arima(1,0,0) (setting optimization to BHHH) Iteration 0: Log likelihood = -3715.2922 Iteration 1: Log likelihood = -3687.2987 Iteration 2: Log likelihood = -3626.5554 Iteration 3: Log likelihood = -3582.3011 Iteration 4: Log likelihood = -3572.3904 (switching optimization to BFGS) Iteration 5: Log likelihood = -3570.8724 Iteration 6: Log likelihood = -3570.7569 Iteration 7: Log likelihood = -3570.7552 Iteration 8: Log likelihood = -3570.7551 Iteration 9: Log likelihood = -3570.7551 ARCH family regression -- AR disturbances Sample: 1 thru 2518 Number of obs = 2518 Wald chi2(1) = 3.77 Log likelihood = -3570.755 Prob > chi2 = 0.0521 ------------------------------------------------------------------------------ | OPG LRET | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- LRET | _cons | .0907315 .016494 5.50 0.000 .058404 .1230591 -------------+---------------------------------------------------------------- ARMA | ar | L1. | -.0412923 .0212565 -1.94 0.052 -.0829542 .0003697 -------------+---------------------------------------------------------------- ARCH | arch | L1. | .1379844 .0185795 7.43 0.000 .1015693 .1743996 L2. | .029216 .0226685 1.29 0.197 -.0152134 .0736454 | garch | L1. | .784434 .0217032 36.14 0.000 .7418964 .8269716 | _cons | .0645645 .0089789 7.19 0.000 .0469662 .0821628 ------------------------------------------------------------------------------ . estat ic Akaike's information criterion and Bayesian information criterion ----------------------------------------------------------------------------- Model | N ll(null) ll(model) df AIC BIC -------------+--------------------------------------------------------------- . | 2,518 . -3570.755 6 7153.51 7188.497 ----------------------------------------------------------------------------- Note: BIC uses N = number of observations. See [R] IC note. . * Osa 2 . arch LRET, arch(1/1) garch(1/1) arima(1,0,0) (setting optimization to BHHH) Iteration 0: Log likelihood = -3706.2766 Iteration 1: Log likelihood = -3619.6382 Iteration 2: Log likelihood = -3580.1158 Iteration 3: Log likelihood = -3571.6851 Iteration 4: Log likelihood = -3571.2074 (switching optimization to BFGS) Iteration 5: Log likelihood = -3571.1761 Iteration 6: Log likelihood = -3571.1652 Iteration 7: Log likelihood = -3571.1652 Iteration 8: Log likelihood = -3571.1652 ARCH family regression -- AR disturbances Sample: 1 thru 2518 Number of obs = 2518 Wald chi2(1) = 3.81 Log likelihood = -3571.165 Prob > chi2 = 0.0511 ------------------------------------------------------------------------------ | OPG LRET | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- LRET | _cons | .0915546 .0164507 5.57 0.000 .0593119 .1237974 -------------+---------------------------------------------------------------- ARMA | ar | L1. | -.041704 .0213751 -1.95 0.051 -.0835985 .0001905 -------------+---------------------------------------------------------------- ARCH | arch | L1. | .1565655 .013794 11.35 0.000 .1295296 .1836013 | garch | L1. | .7992056 .0166879 47.89 0.000 .766498 .8319132 | _cons | .0592067 .0072532 8.16 0.000 .0449907 .0734226 ------------------------------------------------------------------------------ . * Osa 3. Standardiseeritud jääkliikmete leidmine ja nende testimine . predict disp, variance . predict res, residuals (1 missing value generated) . gen sres = res/sqrt(disp) (1 missing value generated) . gen sres_sq = sres^2 (1 missing value generated) . corrgram sres -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial autocor] ------------------------------------------------------------------------------- 1 0.0127 0.0127 .40479 0.5246 | | 2 0.0073 0.0072 .54013 0.7633 | | 3 -0.0261 -0.0263 2.2559 0.5210 | | 4 -0.0092 -0.0086 2.47 0.6500 | | 5 -0.0317 -0.0312 5.0126 0.4143 | | 6 -0.0235 -0.0233 6.4067 0.3792 | | 7 0.0125 0.0131 6.8007 0.4499 | | 8 -0.0229 -0.0247 8.1246 0.4214 | | 9 -0.0056 -0.0070 8.2049 0.5136 | | 10 0.0187 0.0185 9.0873 0.5238 | | 11 0.0045 0.0017 9.1393 0.6090 | | 12 -0.0229 -0.0240 10.471 0.5747 | | 13 -0.0152 -0.0150 11.06 0.6058 | | 14 -0.0184 -0.0193 11.922 0.6126 | | 15 -0.0434 -0.0430 16.686 0.3380 | | 16 0.0366 0.0380 20.083 0.2165 | | 17 0.0349 0.0317 23.18 0.1435 | | 18 0.0090 0.0043 23.387 0.1762 | | 19 -0.0117 -0.0121 23.733 0.2066 | | 20 0.0077 0.0058 23.884 0.2475 | | 21 0.0236 0.0244 25.298 0.2345 | | 22 -0.0478 -0.0454 31.095 0.0942 | | 23 -0.0018 -0.0015 31.104 0.1203 | | 24 0.0016 0.0037 31.11 0.1506 | | 25 -0.0316 -0.0311 33.649 0.1156 | | 26 -0.0378 -0.0382 37.296 0.0703 | | 27 0.0084 0.0041 37.476 0.0865 | | 28 0.0066 0.0025 37.587 0.1065 | | 29 -0.0153 -0.0149 38.186 0.1182 | | 30 0.0003 -0.0027 38.187 0.1450 | | 31 -0.0207 -0.0224 39.284 0.1460 | | 32 -0.0122 -0.0099 39.665 0.1653 | | 33 -0.0153 -0.0171 40.259 0.1798 | | 34 0.0114 0.0044 40.594 0.2025 | | 35 -0.0043 -0.0050 40.642 0.2358 | | 36 0.0107 0.0114 40.933 0.2629 | | 37 0.0162 0.0069 41.606 0.2771 | | 38 0.0063 0.0037 41.708 0.3127 | | 39 0.0267 0.0289 43.539 0.2843 | | 40 0.0187 0.0155 44.431 0.2904 | | . corrgram sres_sq -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial autocor] ------------------------------------------------------------------------------- 1 -0.0082 -0.0082 .1698 0.6803 | | 2 0.0160 0.0159 .81185 0.6664 | | 3 -0.0033 -0.0031 .83983 0.8399 | | 4 0.0220 0.0217 2.059 0.7249 | | 5 -0.0246 -0.0241 3.5829 0.6109 | | 6 0.0144 0.0134 4.1102 0.6618 | | 7 -0.0217 -0.0206 5.2961 0.6239 | | 8 -0.0058 -0.0072 5.3824 0.7160 | | 9 -0.0146 -0.0130 5.9218 0.7477 | | 10 0.0408 0.0397 10.141 0.4282 | | 11 -0.0095 -0.0071 10.372 0.4973 | | 12 -0.0169 -0.0193 11.092 0.5211 | | 13 -0.0068 -0.0060 11.208 0.5934 | | 14 0.0154 0.0136 11.809 0.6216 | | 15 -0.0259 -0.0236 13.505 0.5634 | | 16 0.0327 0.0314 16.21 0.4384 | | 17 0.0043 0.0066 16.258 0.5056 | | 18 -0.0147 -0.0163 16.805 0.5365 | | 19 -0.0089 -0.0072 17.006 0.5895 | | 20 -0.0166 -0.0221 17.71 0.6065 | | 21 -0.0065 -0.0039 17.818 0.6605 | | 22 0.0104 0.0116 18.092 0.7005 | | 23 0.0157 0.0175 18.72 0.7174 | | 24 -0.0177 -0.0191 19.521 0.7237 | | 25 -0.0141 -0.0137 20.029 0.7453 | | 26 -0.0029 -0.0057 20.049 0.7892 | | 27 -0.0060 -0.0080 20.141 0.8248 | | 28 0.0162 0.0196 20.809 0.8332 | | 29 0.0055 0.0072 20.887 0.8632 | | 30 0.0182 0.0183 21.733 0.8636 | | 31 -0.0165 -0.0159 22.43 0.8690 | | 32 -0.0166 -0.0215 23.132 0.8741 | | 33 0.0060 0.0039 23.224 0.8968 | | 34 -0.0050 -0.0026 23.287 0.9169 | | 35 0.0059 0.0096 23.376 0.9332 | | 36 0.0256 0.0267 25.046 0.9148 | | 37 -0.0009 -0.0005 25.049 0.9326 | | 38 0.0480 0.0472 30.942 0.7847 | | 39 0.0045 0.0011 30.993 0.8160 | | 40 0.0201 0.0180 32.024 0.8114 | | . sktest sres Skewness and kurtosis tests for normality ----- Joint test ----- Variable | Obs Pr(skewness) Pr(kurtosis) Adj chi2(2) Prob>chi2 -------------+----------------------------------------------------------------- sres | 2,518 0.0000 0.0000 225.25 0.0000 . * Osa 4, GARCH mudel ja GED jaotus . arch LRET, arch(1/1) garch(1/1) arima(1,0,0)distribution(ged) (setting optimization to BHHH) Iteration 0: Log likelihood = -3706.2766 Iteration 1: Log likelihood = -3572.0222 Iteration 2: Log likelihood = -3502.122 Iteration 3: Log likelihood = -3495.0517 Iteration 4: Log likelihood = -3494.6368 (switching optimization to BFGS) Iteration 5: Log likelihood = -3494.6003 Iteration 6: Log likelihood = -3494.5935 Iteration 7: Log likelihood = -3494.5934 ARCH family regression -- AR disturbances Sample: 1 thru 2518 Number of obs = 2518 Wald chi2(1) = 7.97 Log likelihood = -3494.593 Prob > chi2 = 0.0048 ------------------------------------------------------------------------------ | OPG LRET | Coefficient std. err. z P>|z| [95% conf. interval] -------------+---------------------------------------------------------------- LRET | _cons | .1204195 .0148873 8.09 0.000 .091241 .149598 -------------+---------------------------------------------------------------- ARMA | ar | L1. | -.0565729 .0200421 -2.82 0.005 -.0958547 -.0172912 -------------+---------------------------------------------------------------- ARCH | arch | L1. | .1550116 .0215531 7.19 0.000 .1127683 .197255 | garch | L1. | .8133942 .0242353 33.56 0.000 .7658939 .8608944 | _cons | .0470092 .0102789 4.57 0.000 .0268629 .0671555 -------------+---------------------------------------------------------------- /lnshape | .2321478 .0362397 6.41 0.000 .1611192 .3031764 -------------+---------------------------------------------------------------- shape | 1.261306 .0457094 1.174825 1.354153 ------------------------------------------------------------------------------ . * Osa 6 . display .1550116 + .8133942 .9684058 . * Osa 7, tingimusteta dispersiooni arvutus . display [ARCH]_cons .04700921 . display [ARCH]_cons/(1-([ARCH]L1.arch + [ARCH]L1.garch)) 1.4879062 . * Osa 8, standardiseeritud jääkide testimine lisamooduli armadiag abil . ssc install armadiag . armadiag . armadiag, arch . armadiag, arch table Diagnostics for Square of ARCH standardized residuals Q-stat d.f. corrected for 2 ARCH parameters -1 0 1 -1 0 1 LAG AC PAC Q Prob>Q [Autocorrelation] [Partial Autocor] ------------------------------------------------------------------------------- 1 -0.0052 -0.0052 .06733 | | 2 0.0118 0.0118 .41914 | | 3 -0.0059 -0.0058 .50829 0.4759 | | 4 0.0177 0.0175 1.2971 0.5228 | | 5 -0.0276 -0.0273 3.2268 0.3580 | | 6 0.0070 0.0063 3.3509 0.5009 | | 7 -0.0235 -0.0226 4.7427 0.4481 | | 8 -0.0094 -0.0104 4.9641 0.5484 | | 9 -0.0168 -0.0154 5.6777 0.5778 | | 10 0.0326 0.0315 8.3601 0.3991 | | 11 -0.0105 -0.0088 8.6383 0.4713 | | 12 -0.0205 -0.0226 9.7066 0.4666 | | 13 -0.0118 -0.0115 10.062 0.5248 | | 14 0.0106 0.0087 10.348 0.5855 | | 15 -0.0305 -0.0291 12.708 0.4706 | | 16 0.0317 0.0309 15.262 0.3605 | | 17 0.0018 0.0032 15.27 0.4321 | | 18 -0.0192 -0.0213 16.208 0.4385 | | 19 -0.0130 -0.0116 16.635 0.4794 | | 20 -0.0203 -0.0257 17.679 0.4770 | | 21 -0.0083 -0.0063 17.853 0.5323 | | 22 0.0078 0.0086 18.009 0.5868 | | 23 0.0133 0.0145 18.462 0.6196 | | 24 -0.0200 -0.0218 19.48 0.6155 | | 25 -0.0172 -0.0174 20.234 0.6277 | | 26 -0.0090 -0.0124 20.441 0.6715 | | 27 -0.0073 -0.0101 20.576 0.7160 | | 28 0.0121 0.0148 20.947 0.7447 | | 29 0.0032 0.0042 20.973 0.7876 | | 30 0.0122 0.0112 21.354 0.8103 | | 31 -0.0181 -0.0183 22.186 0.8124 | | 32 -0.0209 -0.0262 23.304 0.8025 | | 33 0.0034 0.0002 23.334 0.8367 | | 34 -0.0068 -0.0051 23.452 0.8636 | | 35 0.0035 0.0061 23.483 0.8895 | | 36 0.0218 0.0228 24.697 0.8787 | | 37 -0.0024 -0.0035 24.712 0.9022 | | 38 0.0436 0.0419 29.58 0.7664 | | 39 0.0031 -0.0015 29.605 0.8011 | | 40 0.0209 0.0192 30.728 0.7928 | | . * Osa 9 . drop disp res sres sres_sq . predict disp, variance . * Osa 10, tingliku dipsersiooni graafik . twoway (tsline disp) (tsline LRET, yaxis(2)) .* Osa 11, tingliku dispersiooni prognoosimine . tsappend, add(100) . predict disp_fc, variance dynamic(2520) . twoway (tsline disp_fc) in 2400/2619 . * Osa 12, keskväärtuse prognoosimine . predict LRET_fc, xb dynamic(2520) . * Osa 13, usalduspiiride leidmine . gen LRET_yp = LRET_fc + 2* sqrt(disp_fc) . gen LRET_ap = LRET_fc - 2* sqrt(disp_fc) . twoway (tsline LRET_fc) (tsline LRET_yp) (tsline LRET_ap) in 2400/2619