# How to use & interpret bivariate GJR-GARCH model with mGJR in R?

I am using a bivariate GJR model using mGJR command "mgarchBEKK" package in R.

The instruction from the package "mgarchBEKK" says I input first time series, second time series, and so on. I am trying to use the unexpected returns as my input and need coefficients from these.

I thought I needed to input my pre-calculated unexpected returns as my first time series, second time series and so on into my model.

However, when I run mGJR, it gives out the output saying $resid1 and $resid2 which look like the residuals (i.e. unexpected returns) which I've been looking for.

1. If so, do I need to input the returns not the unexpected returns into the model to derive the unexpected returns automatically?

2. Besides, how does my bivariate GJR-GARCH model looks like if I try to describe it using the coefficients derived from my output below? How can I get the coefficients for the model that I need for my analysis from the long output I have below? Specifically, I find that I have a total of 17 coefficients where one of them is zero. I find that these coefficients are grouped by 4 where the last one is only one left. However, I am not sure how mathematically these are expressed explicitly within the formal bivariate GJR GARCH formula.

Please note that this is "bivariate" GJR GARCH not just GJR GARCH. Thus, I have 17 parameters where I have 4 blocks each with 4 coefficients plus one parameter making it a total of 17. However, I don't know which parameter corresponds to which variable coefficient. I tried to provide as much information as possible but if any clarification needed please let me know.

The output I get using the expected return is the following:

    > mGJR(eps1, eps2, order = c(1, 1, 1))

Warning: initial values for the parameters are set at:
2 0 2 0.4 0.1 0.1 0.4 0.4 0.1 0.1 0.4 0.1 0.1 0.1 0.1 0.5
Starting estimation process via loglikelihood function implemented in C.
Optimization Method is ' BFGS '
H IS SINGULAR!...
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Estimation process completed.
Starting diagnostics...
Calculating estimated:
1. residuals,
2. correlations,
3. standard deviations,
4. eigenvalues.
Diagnostics ended...
Class attributes are ready via following names:
eps1 eps2 series.length estimation.time total.time order estimation aic asy.se.coef est.params cor sd1 sd2 H.estimated eigenvalues uncond.cov.matrix resid1 resid2
$eps1 [1] -0.002605971 0.110882333 -0.148960989 -0.068514869 -0.003755887 [6] 0.010796054 -0.147830267 0.047830346 0.028587561 0.003945359 [11] 0.082094667 -0.027768830 -0.006713995 0.024364330 -0.012109627 [16] -0.018345875 0.025668553 0.004490535 0.017510124 0.027143473 [21] 0.011606530 0.010522457 0.026053738 0.009380949 -0.070996648 [26] 0.020755072 -0.005830603 0.014289265 -0.000418889 0.022697292 [31] 0.023063329 0.005635615 0.049926161 0.013989454 0.019870327 [36] 0.018279627 0.014478743 -0.002177036 0.024635614 0.050726032 [41] -0.004392337 0.001234857 -0.018066777 -0.054437778 0.010428982 [46] -0.082777078 0.127812102 0.008940764 -0.001295593 0.060328122 [51] -0.009104799 -0.007204478 0.045631975 0.023096514 0.010598574 [56] 0.016541977 -0.011387952 -0.038157908 0.010327360 0.044342365 [61] 0.035077460 0.017492338 0.038596692 0.137205423 -0.004735584 [66] 0.104792896 0.036139814 -0.096482047 -0.000561027 -0.002632458 [71] 0.016177144 0.025230196 0.031753168 0.068971843 0.054021759 [76] 0.027263191 -0.025345373 0.033643409 -0.060322431 0.030377924 [81] -0.069716766 -0.089266804$eps2
[1] -0.002889166  0.003033355 -0.002152031  0.003236581  0.003236581
[6] -0.001602802  0.004961099 -0.003176289 -0.000264979 -0.000264979
[11] -0.000264979 -0.001112752  0.004795299  0.004795299  0.005683859
[16]  0.007793699  0.001613168 -0.000354773  0.001350773 -0.000303199
[21]  0.009337753  0.009337753  0.001886769 -0.001791025  0.005869744
[26]  0.004795546  0.004795546  0.004509183  0.005226653  0.000383686
[31]  0.000207546  0.000207546  0.000207546  0.001570381  0.001669796
[36]  0.000549576  0.000549576 -0.001210093  0.014468461 -0.005345880
[41]  0.000130449  0.000130449 -0.001412638 -0.003304416  0.000117946
[46]  0.002145056  0.002145056 -0.002114632  0.005395410 -0.003153774
[51]  0.001888270 -0.001988031  0.000716514 -0.000331566 -0.000331566
[56] -0.000325350 -0.002882419 -0.006754058 -0.006754058 -0.001131800
[61] -0.017930260  0.002718202  0.006840023  0.006840023  0.002059632
[66]  0.003552300  0.003350965 -0.000126651 -0.000126651 -0.000126651
[71] -0.000990530  0.006430433  0.002933145  0.002933145 -0.002259438
[76]  0.001770744  0.000417412  0.004213458  0.004213458  0.004360485
[81]  0.002158630 -0.000686097

$series.length [1] 82$estimation.time
Time difference of 0.109386 secs

$total.time Time difference of 0.1562669 secs$order
GARCH component  ARCH component   HJR component
1               1               1

$estimation$estimation$par [1] -3.902944e-02 -2.045331e-05 -4.296356e-03 2.268312e-01 2.111034e+00 [6] 1.350601e-04 1.252329e-01 -3.143425e-01 -1.538355e-02 -5.587068e-03 [11] -1.628474e-04 4.224089e-01 1.025256e-01 -7.414033e-03 -4.869328e-01 [16] -1.102507e+00$estimation$value [1] -459.6969$estimation$counts function gradient 278 53$estimation$convergence [1] 0$estimation$message NULL$estimation$hessian [,1] [,2] [,3] [,4] [,5] [1,] 77991.191735 -27033.70607 -1.895287e+03 -655.73521140 -6.727215e+01 [2,] -27033.706072 3337349.78552 -3.369295e+05 -371.07738150 -1.447052e+02 [3,] -1895.286899 -336929.51987 1.109169e+07 -122.26145691 -5.595868e+00 [4,] -655.735211 -371.07738 -1.222615e+02 18.61522485 -1.311354e-02 [5,] -67.272152 -144.70520 -5.595868e+00 -0.01311354 3.109780e-01 [6,] 20.487872 -18111.17773 3.525887e+03 -5.52437237 -8.751496e-02 [7,] -26.898108 -2073.43486 -2.975629e+03 -0.26691407 -3.916406e-01 [8,] 1477.726124 320.50607 -4.807709e+02 -9.98402142 -9.782072e-01 [9,] 9.388141 -27.62368 -5.331019e+01 -0.16106385 -1.537450e-02 [10,] -179.429796 49000.01743 2.023153e+04 7.66772695 1.378254e+00 [11,] 16.757240 -87.91362 2.360375e+03 0.23119576 7.084715e-02 [12,] -317.440585 -56.15303 3.710999e+01 6.57357184 -1.785094e-01 [13,] 3.793978 98.71583 -1.142264e+01 -0.22870343 1.543862e-02 [14,] -146.123961 -9829.15416 -5.196531e+02 -29.62565159 4.260863e-01 [15,] 18.082524 131.52060 3.398486e+03 0.33823287 3.212786e-02 [16,] 11.460530 -240.54059 6.706526e+02 0.32655416 -4.680544e-03 [,6] [,7] [,8] [,9] [,10] [1,] 2.048787e+01 -26.8981081 1477.7261235 9.38814077 -179.429796 [2,] -1.811118e+04 -2073.4348620 320.5060742 -27.62367781 49000.017430 [3,] 3.525887e+03 -2975.6287124 -480.7709387 -53.31018730 20231.529905 [4,] -5.524372e+00 -0.2669141 -9.9840214 -0.16106385 7.667727 [5,] -8.751496e-02 -0.3916406 -0.9782072 -0.01537450 1.378254 [6,] 4.340038e+03 72.0221887 23.7403796 4.74321851 -479.279271 [7,] 7.202219e+01 22.5064989 -0.6280896 0.21674046 -44.382358 [8,] 2.374038e+01 -0.6280896 123.3928335 2.05555317 -53.354577 [9,] 4.743219e+00 0.2167405 2.0555532 20.53760214 53.165201 [10,] -4.792793e+02 -44.3823578 -53.3545766 53.16520102 17583.612011 [11,] -2.045612e+00 1.0454365 38.9154805 -823.29002882 -1763.407498 [12,] -1.488681e+01 -0.5717977 -6.3888226 -0.05658090 -21.965231 [13,] -4.554201e-01 -0.2556849 0.1795778 0.01041940 1.602574 [14,] 2.372186e+02 -13.7297349 13.5989185 -1.51829772 -127.664692 [15,] -1.372792e+01 -1.3537030 0.4896836 0.05291901 12.398407 [16,] -2.586931e+00 -0.1781386 0.1308570 0.05498165 -7.648387 [,11] [,12] [,13] [,14] [,15] [1,] 1.675724e+01 -317.4405852 3.79397825 -146.1239612 18.08252377 [2,] -8.791362e+01 -56.1530304 98.71583141 -9829.1541554 131.52059520 [3,] 2.360375e+03 37.1099898 -11.42263544 -519.6531079 3398.48583556 [4,] 2.311958e-01 6.5735718 -0.22870343 -29.6256516 0.33823287 [5,] 7.084715e-02 -0.1785094 0.01543862 0.4260863 0.03212786 [6,] -2.045612e+00 -14.8868094 -0.45542005 237.2185632 -13.72791768 [7,] 1.045436e+00 -0.5717977 -0.25568491 -13.7297349 -1.35370300 [8,] 3.891548e+01 -6.3888226 0.17957777 13.5989185 0.48968359 [9,] -8.232900e+02 -0.0565809 0.01041940 -1.5182977 0.05291901 [10,] -1.763407e+03 -21.9652313 1.60257372 -127.6646916 12.39840658 [11,] 4.214986e+04 -0.0719787 0.06153061 -11.5769904 1.70462536 [12,] -7.197870e-02 18.7268970 -0.46324902 -16.1849665 1.23612627 [13,] 6.153061e-02 -0.4632490 0.12685032 1.2327783 -0.20692983 [14,] -1.157699e+01 -16.1849665 1.23277827 3180.7362850 -40.24439774 [15,] 1.704625e+00 1.2361263 -0.20692983 -40.2443977 9.65359055 [16,] -1.608423e-01 -0.4136609 0.07688678 13.4226923 0.70015741 [,16] [1,] 1.146053e+01 [2,] -2.405406e+02 [3,] 6.706526e+02 [4,] 3.265542e-01 [5,] -4.680544e-03 [6,] -2.586931e+00 [7,] -1.781386e-01 [8,] 1.308570e-01 [9,] 5.498165e-02 [10,] -7.648387e+00 [11,] -1.608423e-01 [12,] -4.136609e-01 [13,] 7.688678e-02 [14,] 1.342269e+01 [15,] 7.001574e-01 [16,] 2.609256e+00$aic
[1] -443.6969

$asy.se.coef$asy.se.coef[[1]]
[,1]         [,2]
[1,] 0.005951115 0.0006300630
[2,] 0.000000000 0.0003293308

$asy.se.coef[[2]] [,1] [,2] [1,] 0.3150396 0.01581263 [2,] 2.3065406 0.24110204$asy.se.coef[[3]]
[,1]        [,2]
[1,] 0.1049158 0.007811719
[2,] 0.4800751 0.010559776

$asy.se.coef[[4]] [,1] [,2] [1,] 0.2626887 0.01915952 [2,] 3.1255330 0.36661918$asy.se.coef[[5]]
[1] 0.6559587

$est.params$est.params$1 [,1] [,2] [1,] -0.03902944 -2.045331e-05 [2,] 0.00000000 -4.296356e-03$est.params$2 [,1] [,2] [1,] 0.2268312 0.0001350601 [2,] 2.1110340 0.1252329455$est.params$3 [,1] [,2] [1,] -0.31434246 -0.0055870676 [2,] -0.01538355 -0.0001628474$est.params$4 [,1] [,2] [1,] 0.4224089 -0.007414033 [2,] 0.1025256 -0.486932758$est.params$5 [1] -1.102507$cor
[1]           NA  0.031402656  0.058089044 -0.283965989  0.160141195
[6]  0.053237600  0.024081209  0.199587984  0.050169828  0.024045688
[11]  0.022017308  0.015292008 -0.015322752  0.070343728  0.060106129
[16]  0.104828553  0.165459125  0.030923632  0.022277698  0.026315363
[21]  0.020411283  0.102018250  0.102516847  0.035770620  0.024838651
[26]  0.274964544  0.063922572  0.067181338  0.051522997  0.051263760
[31]  0.023492076  0.022088161  0.021845645  0.021179838  0.028180317
[36]  0.028967267  0.023372747  0.022865880  0.020896186  0.180173786
[41]  0.034766653  0.022790880  0.021499773 -0.005938808 -0.137011386
[46]  0.029587448  0.062026969  0.053761176  0.036707465  0.054668898
[51]  0.009740057  0.040966003  0.012100219  0.024982728  0.021599599
[56]  0.021286712  0.020662963 -0.000403477 -0.118423344  0.080086394
[61]  0.017643159  0.287047099  0.043052577  0.095924672  0.129103089
[66]  0.052969944  0.066284046  0.055521350 -0.095508217  0.040009553
[71]  0.022822525  0.020620174  0.080723033  0.044702009  0.051760071
[76]  0.015962034  0.031439947  0.021103665  0.057557712  0.184430145
[81]  0.061929502  0.074235107

$sd1 [1] NA 0.04250885 0.05256355 0.08452372 0.05574627 0.04322082 [7] 0.04134005 0.07735273 0.04624463 0.04210977 0.04121545 0.04524121 [13] 0.04400240 0.04235476 0.04419338 0.04269033 0.04362228 0.04244062 [19] 0.04124873 0.04171567 0.04157849 0.04691775 0.04729332 0.04297800 [25] 0.04133609 0.05057450 0.04475342 0.04245633 0.04322428 0.04275222 [31] 0.04173813 0.04159489 0.04119978 0.04290491 0.04182107 0.04199520 [37] 0.04156416 0.04141240 0.04126752 0.05496396 0.04274670 0.04132509 [43] 0.04113889 0.04241273 0.05098749 0.04227554 0.05554117 0.05507267 [49] 0.04276771 0.04274602 0.04200447 0.04140829 0.04167090 0.04296412 [55] 0.04157519 0.04119998 0.04124952 0.04231602 0.04991076 0.04371888 [61] 0.04217155 0.05092909 0.04333244 0.04758239 0.06275051 0.04389357 [67] 0.05246204 0.04515198 0.06193409 0.04361523 0.04139218 0.04118088 [73] 0.04553376 0.04376651 0.04708736 0.04252185 0.04248968 0.04285559 [79] 0.04458945 0.04858689 0.04500212 0.05183762$sd2
[1]          NA 0.004482407 0.004338972 0.004809936 0.004467527 0.004585295
[7] 0.004308208 0.004536616 0.004338359 0.004304288 0.004302985 0.004303282
[13] 0.004368628 0.004897167 0.004391425 0.005115556 0.005729580 0.004312162
[19] 0.004303200 0.004308760 0.004302868 0.004976847 0.005020608 0.004316566
[25] 0.004309195 0.004939797 0.004398925 0.004894407 0.004397014 0.004840029
[31] 0.004303750 0.004303055 0.004302843 0.004303352 0.004311628 0.004312208
[37] 0.004303962 0.004303769 0.004340892 0.005536457 0.004364419 0.004303177
[43] 0.004302664 0.004381032 0.004754002 0.004305919 0.004331610 0.004329750
[49] 0.004315664 0.004919065 0.004322781 0.004392385 0.004419426 0.004305283
[55] 0.004303278 0.004302883 0.004302743 0.004548148 0.005589150 0.004407496
[61] 0.004305608 0.004895706 0.004332758 0.004476358 0.004463722 0.004425254
[67] 0.004349885 0.004344478 0.004371742 0.004310808 0.004304083 0.004304599
[73] 0.004475105 0.004333152 0.004333715 0.004314340 0.004313605 0.004303264
[79] 0.004365063 0.004618021 0.004372850 0.004343962

$H.estimated , , 1 [,1] [,2] [1,] 2.398788e-03 6.043323e-06 [2,] 6.043323e-06 1.742282e-05 , , 2 [,1] [,2] [1,] 1.807002e-03 5.983524e-06 [2,] 5.983524e-06 2.009197e-05 , , 3 [,1] [,2] [1,] 2.762927e-03 1.324847e-05 [2,] 1.324847e-05 1.882667e-05 , , 4 [,1] [,2] [1,] 0.0071442584 -1.154474e-04 [2,] -0.0001154474 2.313548e-05 , , 5 [,1] [,2] [1,] 3.107646e-03 3.988284e-05 [2,] 3.988284e-05 1.995880e-05 , , 6 [,1] [,2] [1,] 1.868039e-03 1.055064e-05 [2,] 1.055064e-05 2.102493e-05 , , 7 [,1] [,2] [1,] 1.709000e-03 4.288901e-06 [2,] 4.288901e-06 1.856066e-05 , , 8 [,1] [,2] [1,] 5.983444e-03 7.003934e-05 [2,] 7.003934e-05 2.058089e-05 , , 9 [,1] [,2] [1,] 2.138566e-03 1.006536e-05 [2,] 1.006536e-05 1.882135e-05 , , 10 [,1] [,2] [1,] 1.773233e-03 4.358343e-06 [2,] 4.358343e-06 1.852689e-05 , , 11 [,1] [,2] [1,] 1.698713e-03 3.904758e-06 [2,] 3.904758e-06 1.851568e-05 , , 12 [,1] [,2] [1,] 2.046767e-03 2.977135e-06 [2,] 2.977135e-06 1.851824e-05 , , 13 [,1] [,2] [1,] 1.936211e-03 -2.945494e-06 [2,] -2.945494e-06 1.908491e-05 , , 14 [,1] [,2] [1,] 1.793925e-03 1.459058e-05 [2,] 1.459058e-05 2.398224e-05 , , 15 [,1] [,2] [1,] 1.953055e-03 1.166491e-05 [2,] 1.166491e-05 1.928461e-05 , , 16 [,1] [,2] [1,] 1.822465e-03 2.289296e-05 [2,] 2.289296e-05 2.616891e-05 , , 17 [,1] [,2] [1,] 1.902904e-03 4.135442e-05 [2,] 4.135442e-05 3.282809e-05 , , 18 [,1] [,2] [1,] 1.801206e-03 5.659359e-06 [2,] 5.659359e-06 1.859474e-05 , , 19 [,1] [,2] [1,] 1.701457e-03 3.954325e-06 [2,] 3.954325e-06 1.851753e-05 , , 20 [,1] [,2] [1,] 1.740197e-03 4.729997e-06 [2,] 4.729997e-06 1.856541e-05 , , 21 [,1] [,2] [1,] 1.728771e-03 3.651716e-06 [2,] 3.651716e-06 1.851467e-05 , , 22 [,1] [,2] [1,] 2.201275e-03 2.382151e-05 [2,] 2.382151e-05 2.476901e-05 , , 23 [,1] [,2] [1,] 2.236658e-03 2.434172e-05 [2,] 2.434172e-05 2.520650e-05 , , 24 [,1] [,2] [1,] 1.847108e-03 6.636071e-06 [2,] 6.636071e-06 1.863274e-05 , , 25 [,1] [,2] [1,] 1.708672e-03 4.424391e-06 [2,] 4.424391e-06 1.856916e-05 , , 26 [,1] [,2] [1,] 2.557780e-03 6.869377e-05 [2,] 6.869377e-05 2.440159e-05 , , 27 [,1] [,2] [1,] 2.002868e-03 1.258424e-05 [2,] 1.258424e-05 1.935054e-05 , , 28 [,1] [,2] [1,] 1.802540e-03 1.396019e-05 [2,] 1.396019e-05 2.395522e-05 , , 29 [,1] [,2] [1,] 1.868338e-03 9.792344e-06 [2,] 9.792344e-06 1.933373e-05 , , 30 [,1] [,2] [1,] 0.0018277521 1.060760e-05 [2,] 0.0000106076 2.342588e-05 , , 31 [,1] [,2] [1,] 1.742072e-03 4.219893e-06 [2,] 4.219893e-06 1.852227e-05 , , 32 [,1] [,2] [1,] 1.730135e-03 3.953452e-06 [2,] 3.953452e-06 1.851628e-05 , , 33 [,1] [,2] [1,] 1.697422e-03 3.872712e-06 [2,] 3.872712e-06 1.851446e-05 , , 34 [,1] [,2] [1,] 1.840831e-03 3.910538e-06 [2,] 3.910538e-06 1.851884e-05 , , 35 [,1] [,2] [1,] 1.749002e-03 5.081388e-06 [2,] 5.081388e-06 1.859014e-05 , , 36 [,1] [,2] [1,] 1.763597e-03 5.245741e-06 [2,] 5.245741e-06 1.859513e-05 , , 37 [,1] [,2] [1,] 1.727580e-03 4.181164e-06 [2,] 4.181164e-06 1.852409e-05 , , 38 [,1] [,2] [1,] 1.714987e-03 4.075372e-06 [2,] 4.075372e-06 1.852243e-05 , , 39 [,1] [,2] [1,] 1.703008e-03 3.743298e-06 [2,] 3.743298e-06 1.884335e-05 , , 40 [,1] [,2] [1,] 3.021037e-03 5.482789e-05 [2,] 5.482789e-05 3.065235e-05 , , 41 [,1] [,2] [1,] 1.827281e-03 6.486224e-06 [2,] 6.486224e-06 1.904815e-05 , , 42 [,1] [,2] [1,] 1.707763e-03 4.052884e-06 [2,] 4.052884e-06 1.851733e-05 , , 43 [,1] [,2] [1,] 1.692408e-03 3.805606e-06 [2,] 3.805606e-06 1.851292e-05 , , 44 [,1] [,2] [1,] 1.798840e-03 -1.103499e-06 [2,] -1.103499e-06 1.919344e-05 , , 45 [,1] [,2] [1,] 2.599725e-03 -3.321083e-05 [2,] -3.321083e-05 2.260054e-05 , , 46 [,1] [,2] [1,] 1.787221e-03 5.385952e-06 [2,] 5.385952e-06 1.854093e-05 , , 47 [,1] [,2] [1,] 3.084822e-03 1.492262e-05 [2,] 1.492262e-05 1.876285e-05 , , 48 [,1] [,2] [1,] 0.0030329985 1.281940e-05 [2,] 0.0000128194 1.874673e-05 , , 49 [,1] [,2] [1,] 1.829077e-03 6.775136e-06 [2,] 6.775136e-06 1.862496e-05 , , 50 [,1] [,2] [1,] 1.827222e-03 1.149525e-05 [2,] 1.149525e-05 2.419720e-05 , , 51 [,1] [,2] [1,] 1.764375e-03 1.768562e-06 [2,] 1.768562e-06 1.868643e-05 , , 52 [,1] [,2] [1,] 1.714646e-03 7.450944e-06 [2,] 7.450944e-06 1.929305e-05 , , 53 [,1] [,2] [1,] 1.736464e-03 2.228394e-06 [2,] 2.228394e-06 1.953133e-05 , , 54 [,1] [,2] [1,] 1.845916e-03 4.621122e-06 [2,] 4.621122e-06 1.853546e-05 , , 55 [,1] [,2] [1,] 1.728496e-03 3.864375e-06 [2,] 3.864375e-06 1.851820e-05 , , 56 [,1] [,2] [1,] 1.697438e-03 3.773681e-06 [2,] 3.773681e-06 1.851481e-05 , , 57 [,1] [,2] [1,] 1.701523e-03 3.667388e-06 [2,] 3.667388e-06 1.851360e-05 , , 58 [,1] [,2] [1,] 1.790646e-03 -7.765298e-08 [2,] -7.765298e-08 2.068565e-05 , , 59 [,1] [,2] [1,] 2.491084e-03 -3.303522e-05 [2,] -3.303522e-05 3.123859e-05 , , 60 [,1] [,2] [1,] 1.911341e-03 1.543191e-05 [2,] 1.543191e-05 1.942602e-05 , , 61 [,1] [,2] [1,] 1.778439e-03 3.203542e-06 [2,] 3.203542e-06 1.853826e-05 , , 62 [,1] [,2] [1,] 2.593772e-03 7.157055e-05 [2,] 7.157055e-05 2.396793e-05 , , 63 [,1] [,2] [1,] 1.877700e-03 8.083078e-06 [2,] 8.083078e-06 1.877280e-05 , , 64 [,1] [,2] [1,] 2.264084e-03 2.043155e-05 [2,] 2.043155e-05 2.003778e-05 , , 65 [,1] [,2] [1,] 3.937627e-03 3.616188e-05 [2,] 3.616188e-05 1.992481e-05 , , 66 [,1] [,2] [1,] 1.926645e-03 1.028889e-05 [2,] 1.028889e-05 1.958287e-05 , , 67 [,1] [,2] [1,] 2.752265e-03 1.512627e-05 [2,] 1.512627e-05 1.892150e-05 , , 68 [,1] [,2] [1,] 2.038701e-03 1.089117e-05 [2,] 1.089117e-05 1.887449e-05 , , 69 [,1] [,2] [1,] 3.835832e-03 -2.585979e-05 [2,] -2.585979e-05 1.911213e-05 , , 70 [,1] [,2] [1,] 1.902289e-03 7.522472e-06 [2,] 7.522472e-06 1.858307e-05 , , 71 [,1] [,2] [1,] 1.713313e-03 4.065956e-06 [2,] 4.065956e-06 1.852513e-05 , , 72 [,1] [,2] [1,] 1.695865e-03 3.655281e-06 [2,] 3.655281e-06 1.852958e-05 , , 73 [,1] [,2] [1,] 0.0020733237 1.644880e-05 [2,] 0.0000164488 2.002657e-05 , , 74 [,1] [,2] [1,] 0.0019155075 8.477600e-06 [2,] 0.0000084776 1.877621e-05 , , 75 [,1] [,2] [1,] 2.217220e-03 1.056233e-05 [2,] 1.056233e-05 1.878109e-05 , , 76 [,1] [,2] [1,] 1.808108e-03 2.928295e-06 [2,] 2.928295e-06 1.861353e-05 , , 77 [,1] [,2] [1,] 1.805373e-03 5.762429e-06 [2,] 5.762429e-06 1.860719e-05 , , 78 [,1] [,2] [1,] 1.836602e-03 3.891915e-06 [2,] 3.891915e-06 1.851808e-05 , , 79 [,1] [,2] [1,] 1.988219e-03 1.120279e-05 [2,] 1.120279e-05 1.905377e-05 , , 80 [,1] [,2] [1,] 2.360685e-03 4.138156e-05 [2,] 4.138156e-05 2.132612e-05 , , 81 [,1] [,2] [1,] 2.025191e-03 1.218695e-05 [2,] 1.218695e-05 1.912182e-05 , , 82 [,1] [,2] [1,] 2.687139e-03 1.671631e-05 [2,] 1.671631e-05 1.887001e-05$eigenvalues
[1] 4.55569683 0.22879456 0.17683774 0.01426322

$uncond.cov.matrix [,1] [,2] [1,] 0.002266730 0.001058754 [2,] 0.001058754 0.014184073$resid1
[1]  0.000000000  2.606658633 -2.832423405 -0.803429943 -0.076228015
[6]  0.251640690 -3.578761931  0.627605808  0.618572249  0.093834350
[11]  1.992057160 -0.613463505 -0.151066326  0.568366658 -0.281145635
[16] -0.447418119  0.584725959  0.106051164  0.423859148  0.650891694
[21]  0.275002848  0.206027474  0.547710301  0.219653206 -1.720836929
[26]  0.388360723 -0.136578900  0.330299607 -0.015356362  0.530624264
[31]  0.552493411  0.135394145  1.211759017  0.325365217  0.474140365
[36]  0.434967460  0.348083690 -0.051966703  0.590366618  0.941768811
[41] -0.102859959  0.029817748 -0.438515201 -1.283947967  0.205149728
[46] -1.959551678  2.299605523  0.164294634 -0.034506773  1.415352264
[51] -0.217156708 -0.172233261  1.094882761  0.537781247  0.255092253
[56]  0.401673126 -0.274777615 -0.901794851  0.192673354  1.016721711
[61]  0.838610788  0.331314439  0.884670384  2.873061672 -0.079539903
[66]  2.384117962  0.685180049 -2.137240072 -0.009247067 -0.060258875
[71]  0.391339172  0.609775354  0.692992830  1.573446856  1.149792694
[76]  0.640567944 -0.596838960  0.783185773 -1.358186376  0.611629203
[81] -1.552405453 -1.721844943