如何使用 GJR() 来使用和解释双变量 GARCH GJR 模型
How to use & interpret bivariate GARCH GJR model using mGJR()
我正在使用来自 R 的 mGJR() 命令的双变量 GJR 模型。
包"mgarchBEKK"中的说明说我输入第一个时间序列，第二个时间序列，等等。我正在尝试使用意外的 returns 作为我的输入并需要这些系数。
我认为我需要将预先计算的意外 return 作为我的第一个时间序列、第二个时间序列等输入到我的模型中。
然而，当我 运行 mGJR() 时，它给出的输出是“$resid1”和“$resid2”，它们看起来像我的残差（即意外的 returns）一直在寻找。
如果是这样，我是否需要将 return 而不是意外的 return 输入到模型中以自动导出意外的 return？
此外，如果我尝试使用从下面的输出中导出的系数来描述它，我的双变量 GJR GARCH 模型会是什么样子？
如何从下面的长输出中获取分析所需的模型系数？
具体来说，我发现我总共有 17 个系数，其中一个系数为零。我发现这些系数按 4 分组，最后一个只剩下一个。
例如，我找到 $est.params$1、$est.params$2、$est.params$3、$est.params $4, $est.params$5 其中一共有17个参数。
但是，我不确定这些在正式的双变量 GJR GARCH 公式中是如何在数学上明确表达的。
请注意，这是 "bivariate" GJR GARCH 而不仅仅是 GJR GARCH。因此，我有 17 个参数，其中我有 4 个块，每个块有 4 个系数加上一个参数，使它总共有 17 个。但是，我不知道哪个参数对应于哪个变量系数。我尝试提供尽可能多的信息，但如果需要任何说明，请告诉我。
我使用预期的 return 得到的输出如下：
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 '
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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
$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"
我正在尝试复制以下情况：
然后我试图得到如下输出：
mGJR 命令用于估计 GARCH（广义自回归条件异方差）模型。 GARCH 模型用于建模 时间序列的波动性 （最常见的资产 returns）。这（以及许多参数）是您可以从适合的 GJR 对象访问的内容。
如果您想了解更多关于 GARCH 模型与 R 示例配对的信息，我可以推荐以下 R.Tsay 的书籍：
- Analysis of Financial Time Series 和
- Multivariate Time Series Analysis: With R and Financial Applications
do I need to input the returns not the unexpected returns into the model to derive the unexpected returns automatically?
通常 GARCH 模型的输入是过去观察到的 return。 （参见上面引用的书籍或 R. Engle 的 this article，最初提出 ARCH 模型的人）
有一些测试可以确定时间序列中是否存在任何线性相关性。如果有，则需要使用均值模型（例如 VARIMA 模型）将其删除。 Tsays 金融时间序列分析中也有例子和不同的案例。第 133 页很好地解释了波动率模型构建的完整过程。
短： 你的 eps1 和 eps2 需要这些（均值模型校正）return 系列。
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?
需要进行一些挖掘，但在查看 mgarchBEKK 的 publication from Schmidbauer & Roesch (2008) and the code 时，mGJR 规范似乎就是作者 Schmidbauer 和 Roesch 所说的双变量非对称二次 GARCH (baqGARCH) ，在链接出版物的第 5 页上定义为：
拟合的GJR对象的参数以降序表示：C、A、B、Gamma、w。如出版物第 7 页（括号中较小字体的值是 t 值）：
这里是拟合 mGJR 和访问参数的可重现示例：
# packages
library(mgarchBEKK)
# generate heteroscedastic data
dat <- simulateBEKK(series.count = 2, T = 200, c(1,1))
returns1 <- dat$eps[[1]]
returns2 <- dat$eps[[2]]
# fit GJR to data
my_mGJR <- mGJR(eps1 = returns1, eps2 = returns2, order = c(1, 1, 1))
# extract parameters from GJR object
my_param <- my_mGJR$est.params
# assign names
names(my_param) = c('C', 'A', 'B', 'Gamma', 'w')
# access parameters
my_param
举个例子系数矩阵 B、[1,] 和 [2,] 告诉您正在查看矩阵的哪一行，[,1] 和 [,2] 告诉您正在查看矩阵的哪一列。这里有一个过于简单的解释：因为你有一个双变量模型，所以对角线元素 [1,][,1] 和 [2,][,2] 是告诉你关于各自序列的一些关于其自身方差的系数。非对角线元素更多的是关于两个序列的条件协方差或波动溢出。
简而言之： 你有 (2) 的等式 -> 你输入如上所示的系数 -> 你可以求解 H_T（条件协方差矩阵在时间 T) 对于时间因变量 (returnseries_T-1, H_T-1).
Specifically, I find that I have a total of 17 coefficients where one
of them is zero.
如果系数固定为零，则它不算作参数。非对角线较低的系数 C 始终固定为零。因此你总共有 16 个参数（如果你不限制模型，比如作者在他们的论文中所做的那样）。
However, when I run mGJR(), it gives out the output saying "$resid1"
and "$resid2" which look like the residuals
没错，它们是残差，不能用系数解释，但是对于条件波动（不知道你在说什么"unexpected returns"） .它们可以说是模型无法解释的东西，随机白噪声（参见 here or wikipedia）。 GARCH 模型中的残差主要用于执行一些模型充分性测试来回答问题："Does my fitted model adequately explain the conditional variance equation?"
这里是条件波动率、条件相关性和残差图。该系列的条件标准差（前两个图）中似乎存在一些波动率聚类。残差系列（最后两个图）中似乎没有那么多结构。
剧情代码：
library(ggplot2)
library(reshape2)
my_results <- data.frame(index = 1:200,
sd_returns1 = my_mGJR$sd1,
sd_returns2 = my_mGJR$sd2,
cor_returns = my_mGJR$cor,
res_returns1 = my_mGJR$resid1,
res_returns2 = my_mGJR$resid2)
# melt data to long format for plotting
p_results = melt(my_results, id = 'index')
# plot the results
my_p = ggplot(p_results, aes(x = index, y = value)) +
geom_line() +
facet_grid(variable ~ ., scales = "free_y") +
theme_bw()
ggsave('example_cor_sd_res.png', plot = my_p, device = 'png', units = 'cm',
width = 12, height = 15)
I am trying to replicate the following situation:
基本上你有你需要的一切。参数的显着性（p 值或 t 值）可以从参数的标准误差中计算出来。对于 t 值，例如您需要将参数除以标准误差。可以从 GJR 对象中获取标准错误，例如：
my_param_se = my_mGJR$asy.se.coef
names(my_param_se) = paste0(rep("tvals_", 5), c('C', 'A', 'B', 'Gamma', 'w'))
my_param_se
由于 mGJR 命令模型（或 baqGARCH）的构造类似于例如BEKK-GARCH 你可能无法像在你的例子中那样解释它。正如我在上面详细阐述的那样，不同系数的对角线元素将告诉您关于系列 1 创新的系列 1 的显着条件波动 。非对角线元素会告诉您一些关于从一个系列到另一个系列的波动性溢出的信息。如果您想考虑到这一点，您需要将这些结果包含在您的 table 中。
Then I am trying to get the output as below:
我在上面解释了大部分内容，只是对残差的一个注释。看起来模型的充分性是由 LjungBox-Test (=LB?) 衡量的。参见例如here.
我希望这能回答你的问题。
编辑：更新答案以包含其他问题。
我正在使用来自 R 的 mGJR() 命令的双变量 GJR 模型。
包"mgarchBEKK"中的说明说我输入第一个时间序列，第二个时间序列，等等。我正在尝试使用意外的 returns 作为我的输入并需要这些系数。
我认为我需要将预先计算的意外 return 作为我的第一个时间序列、第二个时间序列等输入到我的模型中。
然而，当我 运行 mGJR() 时，它给出的输出是“$resid1”和“$resid2”，它们看起来像我的残差（即意外的 returns）一直在寻找。
如果是这样，我是否需要将 return 而不是意外的 return 输入到模型中以自动导出意外的 return？
此外，如果我尝试使用从下面的输出中导出的系数来描述它，我的双变量 GJR GARCH 模型会是什么样子？ 如何从下面的长输出中获取分析所需的模型系数？ 具体来说，我发现我总共有 17 个系数，其中一个系数为零。我发现这些系数按 4 分组，最后一个只剩下一个。
例如，我找到 $est.params$1、$est.params$2、$est.params$3、$est.params $4, $est.params$5其中一共有17个参数。 但是，我不确定这些在正式的双变量 GJR GARCH 公式中是如何在数学上明确表达的。
请注意，这是 "bivariate" GJR GARCH 而不仅仅是 GJR GARCH。因此，我有 17 个参数，其中我有 4 个块，每个块有 4 个系数加上一个参数，使它总共有 17 个。但是，我不知道哪个参数对应于哪个变量系数。我尝试提供尽可能多的信息，但如果需要任何说明，请告诉我。
我使用预期的 return 得到的输出如下：
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!...
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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
$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"
我正在尝试复制以下情况：
然后我试图得到如下输出：
mGJR 命令用于估计 GARCH（广义自回归条件异方差）模型。 GARCH 模型用于建模 时间序列的波动性 （最常见的资产 returns）。这（以及许多参数）是您可以从适合的 GJR 对象访问的内容。
如果您想了解更多关于 GARCH 模型与 R 示例配对的信息，我可以推荐以下 R.Tsay 的书籍：
- Analysis of Financial Time Series 和
- Multivariate Time Series Analysis: With R and Financial Applications
do I need to input the returns not the unexpected returns into the model to derive the unexpected returns automatically?
通常 GARCH 模型的输入是过去观察到的 return。 （参见上面引用的书籍或 R. Engle 的 this article，最初提出 ARCH 模型的人）
有一些测试可以确定时间序列中是否存在任何线性相关性。如果有，则需要使用均值模型（例如 VARIMA 模型）将其删除。 Tsays 金融时间序列分析中也有例子和不同的案例。第 133 页很好地解释了波动率模型构建的完整过程。
短： 你的 eps1 和 eps2 需要这些（均值模型校正）return 系列。
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?
需要进行一些挖掘，但在查看 mgarchBEKK 的 publication from Schmidbauer & Roesch (2008) and the code 时，mGJR 规范似乎就是作者 Schmidbauer 和 Roesch 所说的双变量非对称二次 GARCH (baqGARCH) ，在链接出版物的第 5 页上定义为：
拟合的GJR对象的参数以降序表示：C、A、B、Gamma、w。如出版物第 7 页（括号中较小字体的值是 t 值）：
这里是拟合 mGJR 和访问参数的可重现示例：
# packages
library(mgarchBEKK)
# generate heteroscedastic data
dat <- simulateBEKK(series.count = 2, T = 200, c(1,1))
returns1 <- dat$eps[[1]]
returns2 <- dat$eps[[2]]
# fit GJR to data
my_mGJR <- mGJR(eps1 = returns1, eps2 = returns2, order = c(1, 1, 1))
# extract parameters from GJR object
my_param <- my_mGJR$est.params
# assign names
names(my_param) = c('C', 'A', 'B', 'Gamma', 'w')
# access parameters
my_param
举个例子系数矩阵 B、[1,] 和 [2,] 告诉您正在查看矩阵的哪一行，[,1] 和 [,2] 告诉您正在查看矩阵的哪一列。这里有一个过于简单的解释：因为你有一个双变量模型，所以对角线元素 [1,][,1] 和 [2,][,2] 是告诉你关于各自序列的一些关于其自身方差的系数。非对角线元素更多的是关于两个序列的条件协方差或波动溢出。
简而言之： 你有 (2) 的等式 -> 你输入如上所示的系数 -> 你可以求解 H_T（条件协方差矩阵在时间 T) 对于时间因变量 (returnseries_T-1, H_T-1).
Specifically, I find that I have a total of 17 coefficients where one of them is zero.
如果系数固定为零，则它不算作参数。非对角线较低的系数 C 始终固定为零。因此你总共有 16 个参数（如果你不限制模型，比如作者在他们的论文中所做的那样）。
However, when I run mGJR(), it gives out the output saying "$resid1" and "$resid2" which look like the residuals
没错，它们是残差，不能用系数解释，但是对于条件波动（不知道你在说什么"unexpected returns"） .它们可以说是模型无法解释的东西，随机白噪声（参见 here or wikipedia）。 GARCH 模型中的残差主要用于执行一些模型充分性测试来回答问题："Does my fitted model adequately explain the conditional variance equation?"
这里是条件波动率、条件相关性和残差图。该系列的条件标准差（前两个图）中似乎存在一些波动率聚类。残差系列（最后两个图）中似乎没有那么多结构。
剧情代码：
library(ggplot2)
library(reshape2)
my_results <- data.frame(index = 1:200,
sd_returns1 = my_mGJR$sd1,
sd_returns2 = my_mGJR$sd2,
cor_returns = my_mGJR$cor,
res_returns1 = my_mGJR$resid1,
res_returns2 = my_mGJR$resid2)
# melt data to long format for plotting
p_results = melt(my_results, id = 'index')
# plot the results
my_p = ggplot(p_results, aes(x = index, y = value)) +
geom_line() +
facet_grid(variable ~ ., scales = "free_y") +
theme_bw()
ggsave('example_cor_sd_res.png', plot = my_p, device = 'png', units = 'cm',
width = 12, height = 15)
I am trying to replicate the following situation:
基本上你有你需要的一切。参数的显着性（p 值或 t 值）可以从参数的标准误差中计算出来。对于 t 值，例如您需要将参数除以标准误差。可以从 GJR 对象中获取标准错误，例如：
my_param_se = my_mGJR$asy.se.coef
names(my_param_se) = paste0(rep("tvals_", 5), c('C', 'A', 'B', 'Gamma', 'w'))
my_param_se
由于 mGJR 命令模型（或 baqGARCH）的构造类似于例如BEKK-GARCH 你可能无法像在你的例子中那样解释它。正如我在上面详细阐述的那样，不同系数的对角线元素将告诉您关于系列 1 创新的系列 1 的显着条件波动 。非对角线元素会告诉您一些关于从一个系列到另一个系列的波动性溢出的信息。如果您想考虑到这一点，您需要将这些结果包含在您的 table 中。
Then I am trying to get the output as below:
我在上面解释了大部分内容，只是对残差的一个注释。看起来模型的充分性是由 LjungBox-Test (=LB?) 衡量的。参见例如here.
我希望这能回答你的问题。
编辑：更新答案以包含其他问题。