0
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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!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    H IS SINGULAR!...
    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

    $resid2
     [1]  0.00000000  0.60291683 -0.34446882  0.47408464  0.74401685 -0.36208567
     [7]  1.22988753 -0.83357295 -0.08954723 -0.06362390 -0.10131479 -0.25004018
    [13]  1.09566787  0.94523475  1.31164457  1.57234641  0.19804905 -0.08528340
    [19]  0.30541107 -0.08591785  2.16540690  1.86518502  0.32642704 -0.42228251
    [25]  1.40120757  0.90215659  1.09997892  0.90303309  1.19070375  0.05489337
    [31]  0.03646646  0.04553108  0.02427045  0.35872374  0.37528677  0.11605970
    [37]  0.12034527 -0.28015423  3.32249290 -1.13529670  0.03315067  0.02970541
    [43] -0.31984221 -0.76117735  0.05094163  0.55098391  0.36347692 -0.49720367
    [49]  1.25203911 -0.71138871  0.43875324 -0.44653544  0.15015921 -0.08924866
    [55] -0.08205853 -0.08336948 -0.66487750 -1.48534156 -1.19469384 -0.33165737
    [61] -4.17835758  0.48521539  1.54523260  1.28097851  0.47447031  0.68879762
    [67]  0.72978029  0.07920992 -0.02991489 -0.02720370 -0.23827852  1.48272617
    [73]  0.60612812  0.61341050 -0.57651419  0.40119127  0.11384865  0.96428797
    [79]  1.03790954  0.85330306  0.58221097 -0.04007542

    attr(,"class")
    [1] "mGJR"
$\endgroup$
  • 1
    $\begingroup$ Why didn't you add a GARCH tag to a question about a GARCH model? This makes it really easy to miss for those users who follow GARCH-related questions and know something about them. $\endgroup$ – Richard Hardy Nov 10 '17 at 17:53
  • $\begingroup$ @Richard Hardy: I did not know that the system had such a tag. I added it please check. $\endgroup$ – Eric Nov 10 '17 at 17:55
  • 1
    $\begingroup$ I had already added it before you, so no problem. Regarding the contents, questions like "how to use an R function" are off topic. What is on topic is part of your question 2, i.e. how to understand and interpret the results. Have you carefully checked the documentation for the package? $\endgroup$ – Richard Hardy Nov 10 '17 at 17:56
  • $\begingroup$ @Richard Hardy: Yes. However, I find four groups with four variables in matrix form and one variable making it a total of 17 parameters. However, I am not sure which one corresponds to which variable in the formal bivariate GJR GARCH model. $\endgroup$ – Eric Nov 10 '17 at 18:15
  • $\begingroup$ @Richard Hardy: For instance, I find $est.params$1, $est.params$2, $est.params$3, $est.params$4, $est.params$5 where there is a total of 17 parameters. $\endgroup$ – Eric Nov 10 '17 at 18:17
1
+50
$\begingroup$

I just noticed that the same question has been posted on Stackoverflow and Cross Validated. The first part of my answer is on Stackoverflow. Since your follow up questions (and most of the original question) have very little to do with actual coding problems I will answer the rest here on Cross Validated. For additional clarity it would help if you update your question here to mirror Stackoverflow.

Part 1: Question and reply

Is here on Stackoverflow.

Part 2: Follow up questions

However I cannot figure out where coefficients such as mu, delta, etc. from my example correspond to which matrix element..

The main problem you are facing is that the model from your description and the model you employed in R are not the same. If you compare the model for the mGJR function (see Schmidbauer & Roesch (2008), P. 5) with what you uploaded, you will see a difference. I'm not familiar with the specification you are trying to replicate.

The mGJR or baqGARCH from the mgarchBEKK package in R, however, is very similar to a BEKK-GARCH model + a form of leverage effect for bivariate timeseries. This means you face the same problems you have with BEKK models, such as the following taken from Multivariate Time Series Analysis: With R and Financial Applications:

[...] limited experience indicates that some of the parameter estimates of a BEKK(1,1) model are statistically insignificant at the traditional 5% level. Yet there exists no simple direct link between the parameters in $A_1$ and $B_1$ and the components of a volatility matrix because the volatility matrix is a nonlinear function of elements of $A_1$ and $B_1$.
Ruey S. Tsay (2014), P. 420.

Back to the baqGARCH. $A$ stands for the "ARCH"-term, $B$ stands for the "GARCH"-term and $\Gamma$ (Gamma) stands for the leverage effect. $\Gamma$ is multiplied with the weighting function $S_w$, which in turn depends on $w$ and the innovations (or returns) in your time series.

For more on the interpretation of the ARCH-term and GARCH-term look for more information regarding multivariate BEKK-GARCH publications (there are plenty). The same applies to the baqGARCH. The construction of $S_w$ and $w$ is described in above mentioned publication by Schmidbauer & Roesch. It appears that the "normal" fit means negative returns in series 1 & 2 lead to the highest weighting of the leverage effect. Depending on the series (and the result for the fitted $w$) this could also change. The results you got $w=-1.102507$ could mean that positive returns in series 2 and negative returns in series 1 lead to the highest leverage effect (in fact I've experimented with that model before and exactly that seems to be the case for negative $w$ values).

I understand it as follows: As a rule of thumb you could say significant diagonal coefficients mean significant ARCH/GARCH/Leverage from the time series innovations on itself. Significant off-diagonal elements mean significant ARCH/GARCH/Leverage spillover between the fitted series 1 & 2.

I'm not sure if there is an exact mapping of the baqGARCH from the mGJR function to the parameters you posted. You would need to get a better understanding of both models.

Also my example does not seem to show the e1*e2 variable while the non-diagonal elements seems to show the coefficients for such variable

As I understand it, $e_1$ and $e_2$ stand for the innovations (returns) in your time series.

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$\endgroup$

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