<div dir="ltr"><div class="gmail-gs" style="margin:0px;padding:0px 0px 20px;width:1504px;font-family:Roboto,RobotoDraft,Helvetica,Arial,sans-serif;font-size:medium"><div class="gmail-"><div id="gmail-:2cy" class="gmail-ii gmail-gt" style="direction:ltr;margin:8px 0px 0px;padding:0px;font-size:0.875rem"><div id="gmail-:2cx" class="gmail-a3s gmail-aiL" style="font-variant-numeric:normal;font-variant-east-asian:normal;font-stretch:normal;font-size:small;line-height:1.5;font-family:Arial,Helvetica,sans-serif;overflow:hidden"><div dir="ltr"><div>Hi,<br></div><div><br></div><div>First of all, let me thank you for the wonderful job you all are doing for our benefit. I am Jyoti Raj Nair, from India and have recently started using R, especially rugarch package for GARCH. I am in a situation, where I need to use external regressors, while using GARCH with 'ged' distribution.</div><div><br></div><div>What I find is, the moment I add the external regressors, I see that the coefficient of the regressor becomes zero with a p-value of 1 and the GARCH term becomes zero as well with a p-value of 1. When I run the same data through Eviews, I note that the GARCH term becomes negative (obviously that is incorrect I think).</div><div><br></div><div>I am enclosing the csv file with the data and I am using an ARIMA model of (6,0,3). I am also pasting the program codes with the output below:</div><div><br></div><div>################## WITH VARIANCE REGRESSOR_1  ############################<br>><br>> set.seed(1)<br>> spec_regressor_1=ugarchspec(mean.model=list(armaOrder=c(6,3),external.regressors=NULL),variance.model = list(garchOrder=c(1,1),external.regressors=matrix(test_file$regressor_1),model="sGARCH"),distribution.model='std')<br>> fit_regressor_1=ugarchfit(spec_regressor_1,data=test_file$returns, out.sample = 0, solver = "hybrid", solver.control = list(),<br>+                       fit.control = list(stationarity = 1, <a href="http://fixed.se/" target="_blank">fixed.se</a> = 0, scale = 0, rec.init = 'all',<br>+                                          trunclag = 1000))<br>> fit_regressor_1<br><br>*---------------------------------*<br>*          GARCH Model Fit        *<br>*---------------------------------*<br><br>Conditional Variance Dynamics<br>-----------------------------------<br>GARCH Model : sGARCH(1,1)<br>Mean Model : ARFIMA(6,0,3)<br>Distribution : std<br><br>Optimal Parameters<br>------------------------------------<br>        Estimate  Std. Error    t value Pr(>|t|)<br>mu      0.046490    0.009023   5.152506 0.000000<br>ar1    -0.304562    0.034959  -8.712062 0.000000<br>ar2    -0.449911    0.030220 -14.887902 0.000000<br>ar3    -0.842745    0.014272 -59.047512 0.000000<br>ar4     0.006586    0.014404   0.457241 0.647498<br>ar5    -0.000777    0.013210  -0.058807 0.953106<br>ar6     0.010526    0.012395   0.849194 0.395773<br>ma1     0.302272    0.032923   9.181110 0.000000<br>ma2     0.456017    0.027290  16.710319 0.000000<br>ma3     0.836477    0.001912 437.598759 0.000000<br>omega   0.008293    0.002490   3.330620 0.000867<br>alpha1  0.054722    0.008109   6.748313 0.000000<br>beta1   0.945127    0.007508 125.887799 0.000000<br><span style="background-color:rgb(255,217,102)">vxreg1  0.000000    0.046051   0.000000 1.000000</span><br>shape   3.400755    0.194712  17.465540 0.000000<br><br>Robust Standard Errors:<br>        Estimate  Std. Error    t value Pr(>|t|)<br>mu      0.046490    0.009397   4.947556 0.000001<br>ar1    -0.304562    0.031777  -9.584348 0.000000<br>ar2    -0.449911    0.028387 -15.849166 0.000000<br>ar3    -0.842745    0.015535 -54.249463 0.000000<br>ar4     0.006586    0.015160   0.434445 0.663965<br>ar5    -0.000777    0.011991  -0.064783 0.948347<br>ar6     0.010526    0.012765   0.824626 0.409584<br>ma1     0.302272    0.029547  10.230229 0.000000<br>ma2     0.456017    0.025565  17.837582 0.000000<br>ma3     0.836477    0.002513 332.874749 0.000000<br>omega   0.008293    0.002867   2.892342 0.003824<br>alpha1  0.054722    0.010927   5.007795 0.000001<br>beta1   0.945127    0.010335  91.450205 0.000000<br><span style="background-color:rgb(255,229,153)">vxreg1  0.000000    0.045982   0.000000 1.000000</span><br>shape   3.400755    0.209648  16.221227 0.000000<br><br>LogLikelihood : -6128.18<br><br>Information Criteria<br>------------------------------------<br>                   <br>Akaike       2.3857<br>Bayes        2.4048<br>Shibata      2.3857<br>Hannan-Quinn 2.3924<br><br>Weighted Ljung-Box Test on Standardized Residuals<br>------------------------------------<br>                         statistic p-value<br>Lag[1]                        2.45  0.1175<br>Lag[2*(p+q)+(p+q)-1][26]     11.70  0.9993<br>Lag[4*(p+q)+(p+q)-1][44]     17.75  0.9202<br>d.o.f=9<br>H0 : No serial correlation<br><br>Weighted Ljung-Box Test on Standardized Squared Residuals<br>------------------------------------<br>                        statistic  p-value<br>Lag[1]                     0.2478 0.618611<br>Lag[2*(p+q)+(p+q)-1][5]   10.0884 0.008738<br>Lag[4*(p+q)+(p+q)-1][9]   12.5385 0.013658<br>d.o.f=2<br><br>Weighted ARCH LM Tests<br>------------------------------------<br>            Statistic Shape Scale P-Value<br>ARCH Lag[3]    0.8764 0.500 2.000  0.3492<br>ARCH Lag[5]    1.8753 1.440 1.667  0.4995<br>ARCH Lag[7]    2.9691 2.315 1.543  0.5194<br><br>Nyblom stability test<br>------------------------------------<br>Joint Statistic:  6.9568<br>Individual Statistics:            <br>mu     0.5652<br>ar1    0.0596<br>ar2    0.6626<br>ar3    0.1377<br>ar4    0.2910<br>ar5    0.5846<br>ar6    0.1087<br>ma1    0.0799<br>ma2    0.6294<br>ma3    0.1554<br>omega  1.3766<br>alpha1 0.6761<br>beta1  0.8438<br>vxreg1 0.3549<br>shape  2.2443<br><br>Asymptotic Critical Values (10% 5% 1%)<br>Joint Statistic:     3.26 3.54 4.07<br>Individual Statistic: 0.35 0.47 0.75<br><br>Sign Bias Test<br>------------------------------------<br>                   t-value   prob sig<br>Sign Bias           1.1788 0.2385    <br>Negative Sign Bias  0.3801 0.7039    <br>Positive Sign Bias  0.2309 0.8174    <br>Joint Effect        1.6430 0.6497    <br><br><br>Adjusted Pearson Goodness-of-Fit Test:<br>------------------------------------<br>  group statistic p-value(g-1)<br>1    20     57.88    8.324e-06<br>2    30     75.30    5.521e-06<br>3    40     79.59    1.341e-04<br>4    50     86.10    8.374e-04<br><br><br>Elapsed time : 3.823148<br><br>><br>> ################ WITH VARIANCE REGRESSOR_2 #########################<br>><br>> set.seed(1)<br>> spec_regressor_2=ugarchspec(mean.model=list(armaOrder=c(6,3),external.regressors=NULL),variance.model = list(garchOrder=c(1,1),external.regressors=matrix(test_file$regressor_2),model="sGARCH"),distribution.model='std')<br>> fit_regressor_2=ugarchfit(spec_regressor_2,data=test_file$returns, out.sample = 0, solver = "hybrid", solver.control = list(),<br>+                           fit.control = list(stationarity = 1, <a href="http://fixed.se/" target="_blank">fixed.se</a> = 0, scale = 0, rec.init = 'all',<br>+                                              trunclag = 1000))<br>> fit_regressor_2<br><br>*---------------------------------*<br>*          GARCH Model Fit        *<br>*---------------------------------*<br><br>Conditional Variance Dynamics<br>-----------------------------------<br>GARCH Model : sGARCH(1,1)<br>Mean Model : ARFIMA(6,0,3)<br>Distribution : std<br><br>Optimal Parameters<br>------------------------------------<br>        Estimate  Std. Error     t value Pr(>|t|)<br>mu      0.056893    0.006314  9.0108e+00 0.000000<br>ar1    -0.386381    0.001677 -2.3041e+02 0.000000<br>ar2    -0.268396    0.001677 -1.6005e+02 0.000000<br>ar3    -0.900510    0.000671 -1.3413e+03 0.000000<br>ar4    -0.010040    0.003353 -2.9944e+00 0.002750<br>ar5     0.010369    0.003919  2.6462e+00 0.008141<br>ar6     0.001257    0.003364  3.7369e-01 0.708633<br>ma1     0.372461    0.000007  5.0185e+04 0.000000<br>ma2     0.261934    0.000002  1.1840e+05 0.000000<br>ma3     0.889388    0.000003  2.8688e+05 0.000000<br><span style="background-color:rgb(255,229,153)">omega   0.000000    0.000079  0.0000e+00 1.000000</span><br>alpha1  0.028093    0.016322  1.7212e+00 0.085211<br><span style="background-color:rgb(255,229,153)">beta1   0.000000    0.006471  0.0000e+00 1.000000</span><br>vxreg1  0.410436    0.017836  2.3011e+01 0.000000<br>shape   4.267964    0.309290  1.3799e+01 0.000000<br><br>Robust Standard Errors:<br>        Estimate  Std. Error     t value Pr(>|t|)<br>mu      0.056893    0.006692     8.50172 0.000000<br>ar1    -0.386381    0.004571   -84.53490 0.000000<br>ar2    -0.268396    0.005127   -52.35384 0.000000<br>ar3    -0.900510    0.001959  -459.64856 0.000000<br>ar4    -0.010040    0.004892    -2.05217 0.040153<br>ar5     0.010369    0.005776     1.79514 0.072632<br>ar6     0.001257    0.003590     0.35009 0.726267<br>ma1     0.372461    0.000020 18325.44524 0.000000<br>ma2     0.261934    0.000008 32098.56753 0.000000<br>ma3     0.889388    0.000013 68274.83047 0.000000<br><span style="background-color:rgb(255,229,153)">omega   0.000000    0.000006     0.00000 1.000000</span><br>alpha1  0.028093    0.050217     0.55943 0.575869<br><span style="background-color:rgb(255,229,153)">beta1   0.000000    0.020105     0.00000 1.000000</span><br>vxreg1  0.410436    0.024166    16.98398 0.000000<br>shape   4.267964    0.672608     6.34540 0.000000<br><br>LogLikelihood : -5709.452<br><br>Information Criteria<br>------------------------------------<br>                   <br>Akaike       2.2231<br>Bayes        2.2422<br>Shibata      2.2231<br>Hannan-Quinn 2.2298<br><br>Weighted Ljung-Box Test on Standardized Residuals<br>------------------------------------<br>                         statistic  p-value<br>Lag[1]                       1.683 0.194577<br>Lag[2*(p+q)+(p+q)-1][26]    14.948 0.008347<br>Lag[4*(p+q)+(p+q)-1][44]    23.716 0.347564<br>d.o.f=9<br>H0 : No serial correlation<br><br>Weighted Ljung-Box Test on Standardized Squared Residuals<br>------------------------------------<br>                        statistic   p-value<br>Lag[1]                      26.93 2.111e-07<br>Lag[2*(p+q)+(p+q)-1][5]    324.77 0.000e+00<br>Lag[4*(p+q)+(p+q)-1][9]    541.03 0.000e+00<br>d.o.f=2<br><br>Weighted ARCH LM Tests<br>------------------------------------<br>            Statistic Shape Scale P-Value<br>ARCH Lag[3]     329.5 0.500 2.000       0<br>ARCH Lag[5]     391.9 1.440 1.667       0<br>ARCH Lag[7]     532.0 2.315 1.543       0<br><br>Nyblom stability test<br>------------------------------------<br>Joint Statistic:  78.6851<br>Individual Statistics:              <br>mu      0.14940<br>ar1     0.06556<br>ar2     0.06370<br>ar3     0.05691<br>ar4     0.06376<br>ar5     0.06364<br>ar6     0.05845<br>ma1     0.05920<br>ma2     0.05870<br>ma3     0.05426<br>omega  72.17748<br>alpha1  5.49804<br>beta1  42.01761<br>vxreg1 13.53124<br>shape   6.78982<br><br>Asymptotic Critical Values (10% 5% 1%)<br>Joint Statistic:     3.26 3.54 4.07<br>Individual Statistic: 0.35 0.47 0.75<br><br>Sign Bias Test<br>------------------------------------<br>                   t-value     prob sig<br>Sign Bias            1.724 0.084679   *<br>Negative Sign Bias   1.589 0.112144    <br>Positive Sign Bias   1.874 0.061044   *<br>Joint Effect        12.630 0.005508 ***<br><br><br>Adjusted Pearson Goodness-of-Fit Test:<br>------------------------------------<br>  group statistic p-value(g-1)<br>1    20     14.49       0.7545<br>2    30     23.92       0.7328<br>3    40     35.17       0.6455<br>4    50     46.49       0.5757<br><br><br>Elapsed time : 4.642887<br><br>><br>> ############## WITH BOTH VARIANCE REGRESSORS ########################<br>><br>> set.seed(1)<br>> regrs_both=cbind(test_file$regressor_1,test_file$regressor_2)<br>> spec_both=ugarchspec(mean.model=list(armaOrder=c(6,3),external.regressors=NULL),variance.model = list(garchOrder=c(1,1),external.regressors=regrs_both,model="sGARCH"),distribution.model='std')<br>> fit_both=ugarchfit(spec_both,data=working_gold$fut_ret, out.sample = 0, solver = "hybrid", solver.control = list(),<br>+                     fit.control = list(stationarity = 1, <a href="http://fixed.se/" target="_blank">fixed.se</a> = 0, scale = 0, rec.init = 'all',<br>+                                        trunclag = 1000))<br>> fit_both<br><br>*---------------------------------*<br>*          GARCH Model Fit        *<br>*---------------------------------*<br><br>Conditional Variance Dynamics<br>-----------------------------------<br>GARCH Model : sGARCH(1,1)<br>Mean Model : ARFIMA(6,0,3)<br>Distribution : std<br><br>Optimal Parameters<br>------------------------------------<br>        Estimate  Std. Error   t value Pr(>|t|)<br>mu      0.056499    0.006218  9.087103 0.000000<br>ar1    -0.861647    0.329725 -2.613229 0.008969<br>ar2    -0.447792    0.384478 -1.164674 0.244151<br>ar3    -0.303149    0.250935 -1.208077 0.227018<br>ar4    -0.009216    0.011431 -0.806279 0.420082<br>ar5     0.011105    0.011176  0.993648 0.320394<br>ar6     0.017919    0.009227  1.941936 0.052145<br>ma1     0.846551    0.329666  2.567903 0.010232<br>ma2     0.428875    0.378405  1.133375 0.257057<br>ma3     0.286646    0.246661  1.162107 0.245192<br><span style="background-color:rgb(255,229,153)">omega   0.000000    0.000078  0.000000 1.000000</span><br>alpha1  0.029239    0.008270  3.535311 0.000407<br><span style="background-color:rgb(249,203,156)">beta1   0.000000    0.011269  0.000000 1.000000<br>vxreg1  0.000000    0.018195  0.000005 0.999996<br></span>vxreg2  0.404066    0.020718 19.503355 0.000000<br>shape   4.362421    0.254501 17.141096 0.000000<br><br>Robust Standard Errors:<br>        Estimate  Std. Error   t value Pr(>|t|)<br>mu      0.056499    0.006035  9.362484 0.000000<br>ar1    -0.861647    0.729126 -1.181753 0.237304<br>ar2    -0.447792    0.673992 -0.664387 0.506442<br>ar3    -0.303149    0.235657 -1.286396 0.198305<br>ar4    -0.009216    0.018479 -0.498731 0.617969<br>ar5     0.011105    0.014195  0.782318 0.434028<br>ar6     0.017919    0.009729  1.841780 0.065507<br>ma1     0.846551    0.729498  1.160458 0.245862<br>ma2     0.428875    0.662109  0.647740 0.517153<br>ma3     0.286646    0.236139  1.213889 0.224790<br><span style="background-color:rgb(255,217,102)">omega   0.000000    0.000001  0.000000 1.000000</span><br>alpha1  0.029239    0.009915  2.948970 0.003188<br><span style="background-color:rgb(255,229,153)">beta1   0.000000    0.024829  0.000000 1.000000<br>vxreg1  0.000000    0.096070  0.000001 0.999999</span><br>vxreg2  0.404066    0.039091 10.336657 0.000000<br>shape   4.362421    0.352650 12.370411 0.000000<br><br>LogLikelihood : -5714.48<br><br>Information Criteria<br>------------------------------------<br>                   <br>Akaike       2.2254<br>Bayes        2.2458<br>Shibata      2.2254<br>Hannan-Quinn 2.2325<br><br>Weighted Ljung-Box Test on Standardized Residuals<br>------------------------------------<br>                         statistic   p-value<br>Lag[1]                       2.132 0.1442055<br>Lag[2*(p+q)+(p+q)-1][26]    15.742 0.0001408<br>Lag[4*(p+q)+(p+q)-1][44]    25.814 0.1705274<br>d.o.f=9<br>H0 : No serial correlation<br><br>Weighted Ljung-Box Test on Standardized Squared Residuals<br>------------------------------------<br>                        statistic   p-value<br>Lag[1]                      26.89 2.151e-07<br>Lag[2*(p+q)+(p+q)-1][5]    325.40 0.000e+00<br>Lag[4*(p+q)+(p+q)-1][9]    543.62 0.000e+00<br>d.o.f=2<br><br>Weighted ARCH LM Tests<br>------------------------------------<br>            Statistic Shape Scale P-Value<br>ARCH Lag[3]     323.3 0.500 2.000       0<br>ARCH Lag[5]     388.7 1.440 1.667       0<br>ARCH Lag[7]     530.5 2.315 1.543       0<br><br>Nyblom stability test<br>------------------------------------<br>Joint Statistic:  90.69<br>Individual Statistics:              <br>mu      0.15586<br>ar1     0.40511<br>ar2     0.05629<br>ar3     0.02915<br>ar4     0.06826<br>ar5     0.15741<br>ar6     0.13758<br>ma1     0.40301<br>ma2     0.05473<br>ma3     0.02894<br>omega  71.73162<br>alpha1  6.23893<br>beta1  38.74346<br>vxreg1 34.53084<br>vxreg2 12.80609<br>shape   6.73046<br><br>Asymptotic Critical Values (10% 5% 1%)<br>Joint Statistic:     3.46 3.75 4.3<br>Individual Statistic: 0.35 0.47 0.75<br><br>Sign Bias Test<br>------------------------------------<br>                   t-value     prob sig<br>Sign Bias            1.890 0.058842   *<br>Negative Sign Bias   1.598 0.110040    <br>Positive Sign Bias   1.709 0.087457   *<br>Joint Effect        12.695 0.005346 ***<br><br><br>Adjusted Pearson Goodness-of-Fit Test:<br>------------------------------------<br>  group statistic p-value(g-1)<br>1    20     19.37      0.43353<br>2    30     35.57      0.18634<br>3    40     54.05      0.05505<br>4    50     51.61      0.37207<br><br><br>Elapsed time : 6.79606 <br></div><div><br></div><div><br></div><div><br></div><div>I would be highly obliged if you could point out where I am wrong..</div><div><br></div><div>Best regards</div><div><br></div><div>J R Nair</div></div><div class="gmail-yj6qo"></div><div class="gmail-adL"></div></div></div><div class="gmail-hq gmail-gt gmail-a10" id="gmail-:2ds" style="font-size:0.875rem;margin:15px 0px;clear:both"><div class="gmail-hp" style="width:1504px;border-top:1px dotted rgb(216,216,216)"></div><div class="gmail-a3I" style="width:1px;height:1px;overflow:hidden">Attachments area</div><div id="gmail-:2dw"></div><div class="gmail-aQH" id="gmail-:2dv" style="padding-top:16px"><div class="gmail-aZK" style="height:0px;overflow:hidden;clear:both"></div></div></div><div class="gmail-hi" style="border-bottom-left-radius:1px;border-bottom-right-radius:1px;padding:0px;width:auto;background:rgb(242,242,242);margin:0px"></div></div></div><br class="gmail-Apple-interchange-newline"></div>