# HW6 output, May 24, 2008. > x=read.table("d-qcom9807.txt") > dim(x) [1] 2514 2 > qcom=log(x[,2]+1) > y=read.table("d-mcd9807.txt") > mcd=log(x[,2]+1) > plot(qcom,type='l') > plot(mcd,type='l') > mcd=log(y[,2]+1) > plot(mcd,type='l') > > qcom=qcom*100 > mcd=mcd*100 > m1=garchOxFit(formula.mean=~arma(0,0),formula.var=~igarch(1,1),series=qcom,include.mean=F,include.var=F) ** SPECIFICATIONS ** ******************** Dependent variable : X Mean Equation : ARMA (0, 0) model. No regressor in the mean Variance Equation : IGARCH (1, 1) model. No regressor in the variance The distribution is a Gauss distribution. Strong convergence using numerical derivatives Log-likelihood = -6331.56 Please wait : Computing the Std Errors ... Maximum Likelihood Estimation (Std.Errors based on Second derivatives) Coefficient Std.Error t-value t-prob ARCH(Alpha1) 0.029567 0.0060123 4.918 0.0000 GARCH(Beta1) 0.970633 No. Observations : 2514 No. Parameters : 2 Mean (Y) : 0.10378 Variance (Y) : 13.19562 Skewness (Y) : 0.52495 Kurtosis (Y) : 9.29522 Log Likelihood : -6331.558 > source("r-garch11v.txt") > m2=garch11v(qcom,0,0,.03,.97) > m2$condvars[2514] [1] 3.320327 > m2$atsq[2514] [1] 0.3108636 > sig=.03*0.311+.97*3.32 > sig [1] 3.22973 > sqrt(3.23) [1] 1.79722 > m2=garchOxFit(formula.mean=~arma(0,0),formula.var=~garch(1,1),series=qcom) ******************** ** SPECIFICATIONS ** ******************** Dependent variable : X Mean Equation : ARMA (0, 0) model. No regressor in the mean Variance Equation : GARCH (1, 1) model. No regressor in the variance The distribution is a Gauss distribution. Strong convergence using numerical derivatives Log-likelihood = -6322.22 Please wait : Computing the Std Errors ... Maximum Likelihood Estimation (Std.Errors based on Second derivatives) Coefficient Std.Error t-value t-prob Cst(M) 0.110362 0.049162 2.245 0.0249 Cst(V) 0.050896 0.021488 2.369 0.0179 ARCH(Alpha1) 0.060624 0.013511 4.487 0.0000 GARCH(Beta1) 0.936262 0.013826 67.72 0.0000 No. Observations : 2514 No. Parameters : 4 Mean (Y) : 0.10378 Variance (Y) : 13.19562 Skewness (Y) : 0.52495 Kurtosis (Y) : 9.29522 Log Likelihood : -6322.224 Alpha[1]+Beta[1]: 0.99669 The sample mean of squared residuals was used to start recursion. The positivity constraint for the GARCH (1,1) is observed. This constraint is alpha[L]/[1 - beta(L)] >= 0. The unconditional variance is 15.3569 The conditions are alpha[0] > 0, alpha[L] + beta[L] < 1 and alpha[i] + beta[i] >= 0. => See Doornik & Ooms (2001) for more details. The condition for existence of the fourth moment of the GARCH is not observed. The constraint equals 1.00073 and should be < 1. => See Ling & McAleer (2001) for details. *********** ** TESTS ** *********** Statistic t-Test P-Value Skewness 0.39365 8.0626 7.4661e-016 Excess Kurtosis 2.5549 26.175 5.0965e-151 Jarque-Bera 748.71 .NaN 2.6292e-163 --------------- Information Criterium (to be minimized) Akaike 5.032795 Shibata 5.032790 Schwarz 5.042071 Hannan-Quinn 5.036162 --------------- Q-Statistics on Standardized Residuals Q( 10) = 10.8284 [0.3710419] Q( 15) = 15.9490 [0.3854489] Q( 20) = 21.8510 [0.3486495] H0 : No serial correlation ==> Accept H0 when prob. is High [Q < Chisq(lag)] -------------- Q-Statistics on Squared Standardized Residuals --> P-values adjusted by 2 degree(s) of freedom Q( 10) = 6.53466 [0.5875652] Q( 15) = 9.74731 [0.7144553] Q( 20) = 16.1481 [0.5822136] H0 : No serial correlation ==> Accept H0 when prob. is High [Q < Chisq(lag)] -------------- ARCH 1-2 test: F(2,2507)= 1.9732 [0.1392] ARCH 1-5 test: F(5,2501)= 0.94572 [0.4501] ARCH 1-10 test: F(10,2491)= 0.67314 [0.7504] -------------- > m2$residuals[2514] [1] -0.66791 > sqrt(m2$condvars[2514]) [1] 1.902577 > m2$condvars[2514] [1] 3.6198 > > m3=garchOxFit(formula.mean=~arma(0,0),formula.var=~garch(1,1),series=qcom,cond.dist="t") ******************** ** SPECIFICATIONS ** ******************** Dependent variable : X Mean Equation : ARMA (0, 0) model. No regressor in the mean Variance Equation : GARCH (1, 1) model. No regressor in the variance The distribution is a Student distribution, with 6.36917 degrees of freedom. Strong convergence using numerical derivatives Log-likelihood = -6250.95 Please wait : Computing the Std Errors ... Maximum Likelihood Estimation (Std.Errors based on Second derivatives) Coefficient Std.Error t-value t-prob Cst(M) 0.056182 0.046299 1.213 0.2251 Cst(V) 0.023352 0.016452 1.419 0.1559 ARCH(Alpha1) 0.041295 0.013079 3.157 0.0016 GARCH(Beta1) 0.957084 0.013316 71.87 0.0000 Student(DF) 6.369168 0.75217 8.468 0.0000 No. Observations : 2514 No. Parameters : 5 Mean (Y) : 0.10378 Variance (Y) : 13.19562 Skewness (Y) : 0.52495 Kurtosis (Y) : 9.29522 Log Likelihood : -6250.952 Alpha[1]+Beta[1]: 0.99838 The sample mean of squared residuals was used to start recursion. The positivity constraint for the GARCH (1,1) is observed. This constraint is alpha[L]/[1 - beta(L)] >= 0. The unconditional variance is 14.4073 The conditions are alpha[0] > 0, alpha[L] + beta[L] < 1 and alpha[i] + beta[i] >= 0. => See Doornik & Ooms (2001) for more details. The condition for existence of the fourth moment of the GARCH is not observed. The constraint equals 1.00449 and should be < 1. => See Ling & McAleer (2001) for details. *********** ** TESTS ** *********** Statistic t-Test P-Value Skewness 0.39354 8.0603 7.6122e-016 Excess Kurtosis 2.5872 26.505 8.4545e-155 Jarque-Bera 766.02 .NaN 4.5796e-167 --------------- Information Criterium (to be minimized) Akaike 4.976891 Shibata 4.976883 Schwarz 4.988486 Hannan-Quinn 4.981099 --------------- Q-Statistics on Standardized Residuals Q( 10) = 11.0024 [0.3573347] Q( 15) = 16.8710 [0.3266361] Q( 20) = 22.5440 [0.3117367] H0 : No serial correlation ==> Accept H0 when prob. is High [Q < Chisq(lag)] -------------- Q-Statistics on Squared Standardized Residuals --> P-values adjusted by 2 degree(s) of freedom Q( 10) = 9.24152 [0.3223335] Q( 15) = 11.5183 [0.5674849] Q( 20) = 18.1869 [0.4434024] H0 : No serial correlation ==> Accept H0 when prob. is High [Q < Chisq(lag)] -------------- ARCH 1-2 test: F(2,2507)= 3.6550 [0.0260]* ARCH 1-5 test: F(5,2501)= 1.6295 [0.1487] ARCH 1-10 test: F(10,2491)= 0.94100 [0.4939] -------------- Diagnostic test based on the news impact curve (EGARCH vs. GARCH) Test P-value Sign Bias t-Test 0.93240 0.35113 Negative Size Bias t-Test 1.53420 0.12498 Positive Size Bias t-Test 0.91692 0.35919 Joint Test for the Three Effects 6.21916 0.10142 --------------- Joint Statistic of the Nyblom test of stability: 1.18108 Individual Nyblom Statistics: Cst(M) 0.08621 Cst(V) 0.08503 ARCH(Alpha1) 0.29051 GARCH(Beta1) 0.20437 Student(DF) 0.41267 Rem: Asymptotic 1% critical value for individual statistics = 0.75. Asymptotic 5% critical value for individual statistics = 0.47. --------------- Adjusted Pearson Chi-square Goodness-of-fit test # Cells(g) Statistic P-Value(g-1) P-Value(g-k-1) 40 45.8727 0.208628 0.084009 50 55.8886 0.231980 0.107851 60 68.4344 0.187608 0.089411 Rem.: k = 5 = # estimated parameters --------------- > m3$residuals[2514] [1] -0.61373 > m3$condvars[2514] [1] 3.6396 > sqrt(m3$condvars[2514]) [1] 1.907774 > > library(evir) Warning message: package 'evir' was built under R version 2.7.0 > qqnorm(qcom) > nqcom=-qcom > mm1=gev(nqcom,block=21) > mm1 $n.all [1] 2514 $n [1] 120 $data [1] 8.144761 16.382684 3.482025 3.591841 3.539094 4.963782 5.946130 [8] 6.309530 10.648337 9.152774 4.662316 6.047532 7.006738 3.492587 [15] 6.482336 13.403323 7.838217 5.675238 8.552194 13.042309 7.721803 [22] 4.804594 5.772552 3.979232 17.863755 5.025278 8.107666 18.449752 [29] 14.033506 14.345591 8.563088 4.108661 5.745752 12.249989 10.298223 [36] 10.243369 14.808594 12.549406 9.738683 11.838947 6.813538 6.687618 [43] 5.794378 5.144804 9.869942 7.152285 5.342715 6.579584 8.227027 [50] 9.977614 6.801442 8.268728 6.543172 7.982381 12.619494 4.545458 [57] 4.472230 4.922806 5.256568 5.678942 4.229913 7.524523 5.377426 [64] 4.974607 3.945002 1.802345 4.465851 2.926199 3.929504 3.654055 [71] 2.807545 1.840331 2.865259 2.186122 3.237031 3.297474 1.727333 [78] 2.612634 3.204913 1.891272 3.963624 4.833662 2.753359 2.523166 [85] 8.349792 2.986145 2.992739 5.038108 1.714006 2.949266 1.301331 [92] 2.961935 2.239695 4.708427 1.381195 2.843137 3.576708 2.929597 [99] 1.441439 1.541419 4.473380 6.592722 4.012536 2.978315 4.760746 [106] 3.664013 4.078762 1.912268 1.802345 5.791941 2.115214 1.877210 [113] 3.376777 1.317136 4.926378 4.576440 1.370042 3.428093 4.264762 [120] 2.844269 $block [1] 21 $par.ests xi sigma mu 0.2405895 2.2225336 3.8516376 $par.ses xi sigma mu 0.09317704 0.19630189 0.23914348 $varcov [,1] [,2] [,3] [1,] 0.008681961 -0.003470978 -0.008627303 [2,] -0.003470978 0.038534431 0.029447154 [3,] -0.008627303 0.029447154 0.057189603 $converged [1] 0 $nllh.final [1] 301.8131 attr(,"class") [1] "gev" > plot(mm1) Make a plot selection (or 0 to exit): 1: plot: Scatterplot of Residuals 2: plot: QQplot of Residuals Selection: 1 Make a plot selection (or 0 to exit): 1: plot: Scatterplot of Residuals 2: plot: QQplot of Residuals Selection: 2 Make a plot selection (or 0 to exit): 1: plot: Scatterplot of Residuals 2: plot: QQplot of Residuals Selection: 0 > mm2=gpd(nqcom,threshold=4.0) > mm2$n.exceed [1] 218 > mm2 $n [1] 2514 $data [1] 8.144761 4.087616 5.678096 4.821593 16.382684 4.963782 4.700566 [8] 4.072929 5.946130 4.002648 4.848671 6.309530 4.723103 6.984323 [15] 10.648337 4.000566 8.201298 9.152774 4.662316 5.419751 6.047532 [22] 4.266327 7.006738 4.115851 6.482336 5.230855 7.212778 10.166956 [29] 13.403323 5.250350 7.838217 4.372621 5.675238 4.683168 8.552194 [36] 13.042309 7.721803 4.804594 5.772552 10.114829 11.056738 9.841249 [43] 4.378367 10.093256 17.863755 8.191095 4.222715 5.017392 4.483838 [50] 5.025278 4.019719 4.459786 4.984592 8.107666 5.905598 7.543501 [57] 9.385584 18.449752 4.093346 4.683168 9.451180 7.608007 6.347562 [64] 7.603259 5.223163 6.217864 8.332509 10.811208 10.644666 4.350476 [71] 14.033506 7.775291 14.345591 13.759220 8.563088 6.950443 4.656345 [78] 4.883737 4.012536 4.108661 4.078137 5.745752 4.231477 4.196431 [85] 4.879011 6.303139 12.249989 9.088688 7.682057 9.447553 4.527565 [92] 5.703183 6.566876 4.829779 10.298223 6.906823 10.243369 10.150352 [99] 7.866990 8.383823 14.808594 6.290466 7.734119 6.122668 4.445149 [106] 4.133463 6.867721 6.016835 6.546909 5.814514 6.243513 7.965378 [113] 12.549406 6.354595 9.738683 7.753893 7.468691 8.834062 9.486908 [120] 11.838947 4.184752 7.160342 9.216683 9.233790 8.151270 4.566809 [127] 6.813538 5.958654 6.687618 5.146805 4.264449 5.403072 4.422361 [134] 4.502875 5.794378 5.228853 5.144804 5.119225 8.046738 9.247610 [141] 9.869942 5.235070 5.936367 6.476148 8.805119 6.655976 5.523368 [148] 7.152285 5.342715 4.655192 5.248664 4.740403 4.243475 5.342926 [155] 6.579584 4.195493 5.032534 8.227027 4.991425 4.012536 4.310481 [162] 4.515742 6.845766 9.977614 6.801442 5.146489 5.405289 6.171584 [169] 8.268728 5.552540 4.777948 4.639164 5.755179 6.441266 5.587218 [176] 6.543172 7.982381 6.612805 6.365571 4.956111 4.153371 5.045470 [183] 12.619494 7.047504 7.305468 4.515114 4.545458 4.472230 4.922806 [190] 5.256568 4.503712 5.678942 4.229913 7.524523 4.082199 5.048836 [197] 5.377426 4.738096 4.974607 4.465851 4.833662 4.068034 4.619788 [204] 8.349792 5.038108 4.096159 4.708427 4.473380 5.318561 6.592722 [211] 4.649744 4.012536 4.760746 4.078762 5.791941 4.926378 4.576440 [218] 4.264762 $threshold [1] 4 $p.less.thresh [1] 0.9132856 $n.exceed [1] 218 $method [1] "ml" $par.ests xi beta 0.01627922 2.59133967 $par.ses xi beta 0.07768986 0.26704696 $varcov [,1] [,2] [1,] 0.006035714 -0.01544255 [2,] -0.015442547 0.07131408 $information [1] "observed" $converged [1] 0 $nllh.final [1] 429.1355 attr(,"class") [1] "gpd" > shape(nqcom) > riskmeasures(mm2,c(0.95,0.99,0.999)) p quantile sfall [1,] 0.950 5.433197 8.091137 [2,] 0.990 9.696960 12.425460 [3,] 0.999 15.994580 18.827297 > Thredhold = 5.0 > mm3=gpd(nqcom,threshold=5.0) > mm3 $n [1] 2514 $data [1] 8.144761 5.678096 16.382684 5.946130 6.309530 6.984323 10.648337 [8] 8.201298 9.152774 5.419751 6.047532 7.006738 6.482336 5.230855 [15] 7.212778 10.166956 13.403323 5.250350 7.838217 5.675238 8.552194 [22] 13.042309 7.721803 5.772552 10.114829 11.056738 9.841249 10.093256 [29] 17.863755 8.191095 5.017392 5.025278 8.107666 5.905598 7.543501 [36] 9.385584 18.449752 9.451180 7.608007 6.347562 7.603259 5.223163 [43] 6.217864 8.332509 10.811208 10.644666 14.033506 7.775291 14.345591 [50] 13.759220 8.563088 6.950443 5.745752 6.303139 12.249989 9.088688 [57] 7.682057 9.447553 5.703183 6.566876 10.298223 6.906823 10.243369 [64] 10.150352 7.866990 8.383823 14.808594 6.290466 7.734119 6.122668 [71] 6.867721 6.016835 6.546909 5.814514 6.243513 7.965378 12.549406 [78] 6.354595 9.738683 7.753893 7.468691 8.834062 9.486908 11.838947 [85] 7.160342 9.216683 9.233790 8.151270 6.813538 5.958654 6.687618 [92] 5.146805 5.403072 5.794378 5.228853 5.144804 5.119225 8.046738 [99] 9.247610 9.869942 5.235070 5.936367 6.476148 8.805119 6.655976 [106] 5.523368 7.152285 5.342715 5.248664 5.342926 6.579584 5.032534 [113] 8.227027 6.845766 9.977614 6.801442 5.146489 5.405289 6.171584 [120] 8.268728 5.552540 5.755179 6.441266 5.587218 6.543172 7.982381 [127] 6.612805 6.365571 5.045470 12.619494 7.047504 7.305468 5.256568 [134] 5.678942 7.524523 5.048836 5.377426 8.349792 5.038108 5.318561 [141] 6.592722 5.791941 $threshold [1] 5 $p.less.thresh [1] 0.9435163 $n.exceed [1] 142 $method [1] "ml" $par.ests xi beta -0.06256969 2.96976811 $par.ses xi beta 0.08499626 0.35440209 $varcov [,1] [,2] [1,] 0.007224365 -0.02268666 [2,] -0.022686660 0.12560084 $information [1] "observed" $converged [1] 0 $nllh.final [1] 287.6947 attr(,"class") [1] "gpd" > riskmeasures(mm3,c(0.95,0.99,0.999)) p quantile sfall [1,] 0.950 5.360723 8.134374 [2,] 0.990 9.873042 12.380985 [3,] 0.999 15.587583 17.759023 > ************* MCD data > mm=garchOxFit(formula.mean=~arma(0,0),formula.var=~igarch(1,1),series=mcd,include.mean=F,include.var=F) ******************** ** SPECIFICATIONS ** ******************** Dependent variable : X Mean Equation : ARMA (0, 0) model. No regressor in the mean Variance Equation : IGARCH (1, 1) model. No regressor in the variance The distribution is a Gauss distribution. Strong convergence using numerical derivatives Log-likelihood = -4885.22 Please wait : Computing the Std Errors ... Maximum Likelihood Estimation (Std.Errors based on Second derivatives) Coefficient Std.Error t-value t-prob ARCH(Alpha1) 0.036463 0.0047638 7.654 0.0000 GARCH(Beta1) 0.963737 No. Observations : 2514 No. Parameters : 2 Mean (Y) : 0.04155 Variance (Y) : 3.31628 Skewness (Y) : -0.06057 Kurtosis (Y) : 7.64644 Log Likelihood : -4885.216 --------------- > mm=garch11v(mcd,0,0,0.036,0.964) > mm$condvars[2514] [1] 1.717335 > mm$atqs[2514] NULL > mm$atsq[2514] [1] 0.9931101 > tt=0.036*mm$atsq[2514]+0.936*mm$condvars[2514] > tt [1] 1.643177 > VaR = 2.33*sqrt(tt) > VaR [1] 2.986745 > > nmcd=-mcd > meplot(nmcd) > mma=gev(nmcd,block=21) > mma $n.all [1] 2514 $n [1] 120 $data [1] 2.1798878 2.5522957 3.0199447 4.5009918 1.8868903 2.6872863 [7] 3.7378970 10.6136372 4.5561332 3.1815797 3.9740288 3.7124671 [13] 3.3458546 1.6173082 4.1263759 3.4616290 2.8618634 2.4692363 [19] 1.7595904 3.3540238 1.4492511 4.8420582 3.1498923 3.3993280 [25] 11.1133816 3.9067285 6.1588211 6.2131820 4.9029543 5.6225437 [31] 2.9500904 2.9558582 5.4435067 5.5689258 5.3345926 4.6700699 [37] 6.4792420 2.5633755 3.1225480 3.2427122 2.3875771 4.4011450 [43] 1.9026868 1.3281814 4.0456436 5.9416727 2.7008467 3.2991276 [49] 3.4531405 2.0775320 3.7271015 1.4492511 1.4805056 2.3419099 [55] 8.4223267 3.7509778 13.7160828 5.8633855 8.1986930 8.3356609 [61] 5.1640723 3.1346199 4.3242630 2.7787522 6.8953587 2.2472629 [67] 3.9074564 2.6406606 2.4107259 2.3327994 2.6836910 5.3627596 [73] 2.3455953 1.8255625 2.3978193 4.5964361 1.7234667 1.5645759 [79] 2.0293528 1.9157336 2.7749480 1.3272694 2.1941974 0.9932161 [85] 1.8161934 2.8785351 1.6307243 1.8881132 2.8010661 1.5628491 [91] 1.3372008 4.2396150 3.7480708 3.9042329 1.9902752 1.8882151 [97] 1.9434635 1.1154986 1.0596950 1.5324828 1.7449358 3.0525189 [103] 1.9110447 2.3015844 1.3569653 1.9450949 1.8800629 1.2468409 [109] 2.6619167 2.9694551 2.7001276 1.3781531 1.7872771 2.2156656 [115] 2.9068422 1.6920345 1.4847683 2.3028124 1.9860929 2.3560379 $block [1] 21 $par.ests xi sigma mu 0.3216466 1.0450397 2.2926272 $par.ses xi sigma mu 0.09023907 0.09507533 0.11098755 $varcov [,1] [,2] [,3] [1,] 0.0081430889 -0.0005927476 -0.003369672 [2,] -0.0005927476 0.0090393182 0.007004418 [3,] -0.0033696716 0.0070044180 0.012318235 $converged [1] 0 $nllh.final [1] 216.6527 attr(,"class") [1] "gev" > mmb=gev(nmcd,block=63) > mmb $n.all [1] 2514 $n [1] 40 $data [1] 3.019945 4.500992 10.613637 3.974029 4.126376 3.461629 3.354024 [8] 4.842058 11.113382 6.213182 5.443507 5.568926 6.479242 4.401145 [15] 4.045644 5.941673 3.727102 2.341910 13.716083 8.335661 5.164072 [22] 6.895359 3.907456 5.362760 2.397819 4.596436 2.774948 2.194197 [29] 2.878535 2.801066 4.239615 3.904233 1.943464 3.052519 2.301584 [36] 1.945095 2.969455 2.215666 2.906842 2.356038 $block [1] 63 $par.ests xi sigma mu 0.3846406 1.2565516 3.2215759 $par.ses xi sigma mu 0.1849680 0.2129951 0.2398092 $varcov [,1] [,2] [,3] [1,] 0.03421318 -0.00560349 -0.01763779 [2,] -0.00560349 0.04536690 0.03665300 [3,] -0.01763779 0.03665300 0.05750844 $converged [1] 0 $nllh.final [1] 80.90165 attr(,"class") [1] "gev" > > evtVaR(.385,1.257,3.222,63,.01) [1] 3.850105 > evtVaR(.322,1.045,2.293,21,.01) [1] 4.403203 > mmc=gpd(nmcd,threshold=3.0) > mmc $n [1] 2514 $data [1] 3.019945 4.500992 3.737897 3.328898 3.343476 10.613637 3.755338 [8] 3.797293 4.556133 3.181580 3.024789 3.974029 3.712467 3.315252 [15] 3.345855 4.126376 3.944170 3.288379 3.461629 3.354024 4.194346 [22] 4.842058 3.149892 3.399328 3.030561 3.298611 11.113382 3.119866 [29] 3.088301 3.774029 3.906728 5.494733 6.158821 4.136277 3.716619 [36] 6.213182 3.588628 4.902954 4.277807 3.780260 3.196240 5.622544 [43] 3.043756 5.443507 5.568926 3.509157 5.334593 3.027469 4.670070 [50] 3.110993 6.479242 4.141384 3.122548 3.242712 4.401145 3.532981 [57] 4.045644 5.941673 4.844157 3.299128 3.453141 3.263890 3.727102 [64] 3.815368 3.665880 8.422327 3.674075 3.750978 3.120588 3.490516 [71] 4.946969 13.716083 4.046997 3.941673 5.863385 3.149892 8.198693 [78] 4.014306 4.408878 3.223398 8.335661 5.164072 3.134620 4.324263 [85] 6.895359 3.907456 3.028397 5.362760 4.596436 4.239615 3.748071 [92] 3.904233 3.052519 $threshold [1] 3 $p.less.thresh [1] 0.9630072 $n.exceed [1] 93 $method [1] "ml" $par.ests xi beta 0.2489196 1.0623335 $par.ses xi beta 0.1310634 0.1754145 $varcov [,1] [,2] [1,] 0.01717761 -0.01469981 [2,] -0.01469981 0.03077026 $information [1] "observed" $converged [1] 0 $nllh.final [1] 121.7857 attr(,"class") [1] "gpd" > riskmeasures(mmc,c(0.95,0.99,0.999)) p quantile sfall [1,] 0.950 2.691629 4.003837 [2,] 0.990 4.642630 6.601430 [3,] 0.999 9.216464 12.691104 >