How to use & interpret bivariate GARCH GJR model using mGJR() - r
I am using a bivariate GJR model using mGJR() command from 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.
If so, do I need to input the returns not the unexpected returns into the model to derive the unexpected returns automatically?
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.
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.
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 '
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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"
I am trying to replicate the following situation:
Then I am trying to get the output as below:
The mGJR command is used to estimate a GARCH (Generalized autoregressive conditional heteroscedasticity) model. GARCH models are used to model volatility of time-series (most commonly asset returns). That (and lots of parameters) is what you can access from the fitted GJR object.
If you want to know more about GARCH models paired with examples in R, I can recommend the following books by R. Tsay:
Analysis of Financial Time Series and
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?
Usually the input for GARCH models are in the past observed returns. (see e.g. the above quoted books or this article by R. Engle, the person who initially proposed the ARCH model)
There are some tests to determine if there are any linear dependencies in the time series. If there are, they need to be removed with a mean-model (such as VARIMA models). Examples and different cases are also in Tsays Analysis of Financial Time Series. The full process for volatility model building is nicely explained on page 133.
Short: Your eps1 and eps2 need to be these (mean-model corrected) return series.
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?
It takes a bit of digging but when looking at a publication from Schmidbauer & Roesch (2008) and the code of the mgarchBEKK it looks like the mGJR specification is what the authors Schmidbauer & Roesch call a bivariate asymmetric quadratic GARCH (baqGARCH), which on page 5 of linked publication is defined as:
The parameters from the fitted GJR object represent in descending order: C, A, B, Gamma, w. as on page 7 of the publication (the values in smaller font in the parenthesis are t-values):
Here a reproducible example for fitting mGJR and accessing the parameters:
# 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
Take e.g. the coefficient-matrix B, [1,] and [2,] tell you which row, [,1] and [,2] which column of the matrix you are looking at. Here an oversimplified explanation: Since you have a bivariate model the diagonal elements [1,][,1] and [2,][,2] are the coefficients that tell you something about the respective series on its own variance. The off-diagonal elements are more about the conditional covariance or volatility spillover of the two series.
Short: You have the equation from (2) -> You input the coefficients as shown above -> You can solve for H_T (conditional covariance matrix at time T) for the time dependant variables (returnseries_T-1, H_T-1).
Specifically, I find that I have a total of 17 coefficients where one
of them is zero.
If a coefficient is fixed to zero it doesn't count as a parameter. The off-diagonal lower coefficient C is always fixed to zero. Thus you have a total of 16 parameters (if you don't restrict the model, such as the authors have done in their paper).
However, when I run mGJR(), it gives out the output saying "$resid1"
and "$resid2" which look like the residuals
That is correct, they are the residuals that are not explained by the coefficients, but for the conditional volatility (not sure what you are on about "unexpected returns"). They are so to speak what cannot be explained by the model, random white noise (see e.g. here or wikipedia). Residuals in GARCH models are mostly used to perform some model adequacy tests to answer the question: "Does my fitted model adequately explain the conditional variance equation?"
Here a plot of the conditional volatility, conditional correlation and the residuals. There seem to be some volatility clustering in the conditional standarddeviation of the series (first two plots). There doesn't seem to be quite as much structure in the residual series (last two plots).
And the code for the plot:
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$resid2)
# melt data to long format for plotting
p_results = melt(my_results, id = 'index')
# plot the results
my_p = ggplot(p_results, aes(x = index, y = value)) +
geom_line() +
facet_grid(variable ~ ., scales = "free_y") +
theme_bw()
ggsave('example_cor_sd_res.png', plot = my_p, device = 'png', units = 'cm',
width = 12, height = 15)
I am trying to replicate the following situation:
Basically you have everything you need. Significance of the parameters (either p-values or t-values) can be calculated from the standard errors of the parameters. For the t-values e.g. you need to divide the parameters by the standard errors. The standard errors can be taken from the GJR object like:
my_param_se = my_mGJR$asy.se.coef
names(my_param_se) = paste0(rep("tvals_", 5), c('C', 'A', 'B', 'Gamma', 'w'))
my_param_se
Since the mGJR commands model (or baqGARCH) is similarly constructed as e.g. the BEKK-GARCH you probably won't be able to interpret it the same way as in your example. As I've elaborated above the diagonal elements of the different coefficients will tell you about significant conditional volatility of series 1 from innovations in series 1. The off-diagonal elements will tell you something about volatility-spillover from one series to the other. If you want to account for that you will need to include these results in your table.
Then I am trying to get the output as below:
Most of this I explained above, just one note to the residuals. It looks like the model adequacy was gauged by the LjungBox-Test (=LB?). See e.g. here.
I hope this answers your questions.
Edit: updated answer to include the additional questions.
Related
How to generate random numbers with normal distribution and uniform distribution
I am a newbie in R. Now, I want to create a matrix, and then extract 20 random Numbers from each of these three uniform distributions: U(0.6,0.8), U(0.0001,0.0003), U(100,110), and place them in the first three columns of the matrix, with each column corresponding to a uniform distribution. Then 20 random Numbers are extracted from each of the two normal distributions: N(7750,0.01), N(12,0.4), and placed in the last two columns of the matrix. My program is as follows, but can only achieve uniform distribution of random numbers, cannot achieve the first three columns are uniform distribution, the last two columns are the normal distribution of random numbers, How can I change it?
input <-5 # variable input
xinput <- 20 #sampling number
range <- matrix(c(0.60,0.80,
0.0001,0.0003,
100,110,
7700,8000,
10,15,
),nrow=input,ncol=2,byrow=TRUE)
range
rangeresult <- matrix(0, nrow=xinput, ncol=input)# empty matrix for latter data
rangeresult
##uniform distribution
for (i in 1:input){
set.seed(456+i) # make results reproducible
rangeresult[,i] <- runif(xinput,range[i,1],range[i,2])
}
Perhaps try this cbind( u1 = runif(20L, 0.6, 0.8), u2 = runif(20L, 0.0001, 0.0003), u3 = runif(20L, 100, 110), n1 = rnorm(20L, 7750, 0.01), n2 = rnorm(20L, 12, 0.4) ) Output u1 u2 u3 n1 n2 [1,] 0.7558480 0.0002851074 101.7209 7749.988 11.75270 [2,] 0.7807589 0.0002600877 104.9278 7749.998 11.67970 [3,] 0.7480385 0.0001562960 109.5744 7749.979 11.84603 [4,] 0.6283492 0.0001408027 108.9455 7749.999 12.00459 [5,] 0.7666862 0.0002485003 106.4735 7750.002 12.58783 [6,] 0.6354397 0.0001042544 107.0999 7749.982 12.36555 [7,] 0.7340912 0.0002507386 109.7052 7749.994 11.75111 [8,] 0.7220797 0.0001173221 105.7116 7749.995 11.35322 [9,] 0.6956138 0.0001478050 104.6444 7750.004 11.68879 [10,] 0.6146491 0.0001238944 108.5946 7750.006 12.78417 [11,] 0.7436676 0.0002492057 107.6073 7750.003 11.80814 [12,] 0.7916866 0.0001927277 100.1949 7750.016 12.16362 [13,] 0.7701075 0.0002236796 103.9207 7750.007 11.82555 [14,] 0.7151522 0.0001528767 101.0997 7749.996 11.75938 [15,] 0.6866158 0.0002872521 100.7036 7750.018 11.36261 [16,] 0.6106267 0.0001278512 105.8946 7749.986 11.81682 [17,] 0.6537794 0.0002875799 104.2015 7750.007 11.56224 [18,] 0.6095022 0.0001534366 108.9352 7749.993 12.22691 [19,] 0.7156714 0.0001303851 107.7274 7749.995 12.01923 [20,] 0.6397735 0.0002706792 109.6200 7749.986 12.01927
matrix( c(runif(20, .6, .8), runif(20, .0001, .0003), runif(20, 100, 110), rnorm(20, 7750, .01), rnorm(20, 12, .4)), ncol=5) #> [,1] [,2] [,3] [,4] [,5] #> [1,] 0.6303004 0.0002700728 102.6577 7750.008 12.10271 #> [2,] 0.7611678 0.0001594420 106.2736 7750.001 11.95071 #> [3,] 0.7217263 0.0002726162 105.9933 7749.993 12.16880 #> [4,] 0.7873636 0.0001409666 109.9674 7750.016 11.58212 #> [5,] 0.7329912 0.0002504620 105.8886 7750.005 11.62768 #> [6,] 0.6775068 0.0002546660 109.9630 7750.000 11.75542 #> [7,] 0.6927353 0.0001217041 105.5130 7750.004 12.46987 #> [8,] 0.7889347 0.0001849753 105.8204 7750.002 11.96011 #> [9,] 0.7555766 0.0001712631 104.6053 7750.013 12.77534 #> [10,] 0.6225500 0.0001441519 101.4559 7750.011 11.62323 #> [11,] 0.6004412 0.0002862156 100.7426 7750.015 12.34398 #> [12,] 0.7896445 0.0001871342 103.5566 7750.002 11.18040 #> [13,] 0.7995510 0.0002998966 101.2008 7750.005 11.79095 #> [14,] 0.7271423 0.0001385434 108.3129 7750.006 11.85577 #> [15,] 0.7990341 0.0001868429 102.3255 7749.974 12.00426 #> [16,] 0.7711383 0.0001362412 108.1071 7749.995 11.62242 #> [17,] 0.7168780 0.0001821163 103.0949 7750.021 12.35856 #> [18,] 0.7197489 0.0002015831 109.4623 7749.981 11.46613 #> [19,] 0.7006335 0.0001257633 100.9744 7750.001 12.03066 #> [20,] 0.7503335 0.0002953110 102.1582 7749.989 12.54394
Calculate P values from Auto Arima model summary
I have generated an Auto Arima model. The model specification of the output is as shown below :- ts_regr_auto_new_objects[[1]]$model $phi [1] 0.7543751 -0.6873447 0.5583951 $theta [1] 0.06711257 0.66005781 0.18953643 $Delta numeric(0) $Z [1] 1 0 0 0 $a [1] -2755.5419 -301.0682 -1891.6939 -266.0682 $P [,1] [,2] [,3] [,4] [1,] 0 0.000000e+00 0.000000e+00 0.000000e+00 [2,] 0 -6.938894e-18 -2.775558e-17 -8.673617e-18 [3,] 0 -2.775558e-17 1.110223e-16 2.775558e-17 [4,] 0 -8.673617e-18 2.775558e-17 6.938894e-18 $T [,1] [,2] [,3] [,4] [1,] 0.7543751 1 0 0 [2,] -0.6873447 0 1 0 [3,] 0.5583951 0 0 1 [4,] 0.0000000 0 0 0 $V [,1] [,2] [,3] [,4] [1,] 1.00000000 0.067112571 0.66005781 0.18953643 [2,] 0.06711257 0.004504097 0.04429818 0.01272028 [3,] 0.66005781 0.044298176 0.43567631 0.12510500 [4,] 0.18953643 0.012720277 0.12510500 0.03592406 $h [1] 0 $Pn [,1] [,2] [,3] [,4] [1,] 1.00000000 0.067112571 0.66005781 0.18953643 [2,] 0.06711257 0.004504097 0.04429818 0.01272028 [3,] 0.66005781 0.044298176 0.43567631 0.12510500 [4,] 0.18953643 0.012720277 0.12510500 0.03592406 The model summary is as shown below :- summary(ts_regr_auto_new_objects[[1]]) Series: histmodellingdataxtsobjects[[i]]$usage Regression with ARIMA(3,0,3) errors Coefficients: ar1 ar2 ar3 ma1 ma2 ma3 intercept temp new_wday_ind S1.365 C1.365 S1.7 C1.7 0.7544 -0.6873 0.5584 0.0671 0.6601 0.1895 20148.1783 -255.7988 1002.2502 4591.0172 -1603.2133 242.1379 -378.4656 s.e. 0.1216 0.1551 0.0991 0.1285 0.1186 0.0742 530.3229 24.0099 190.2674 437.2782 393.9352 104.1117 129.0343 sigma^2 estimated as 1263859: log likelihood=-3244.91 AIC=6517.82 AICc=6518.96 BIC=6573.17 Training set error measures: ME RMSE MAE MPE MAPE MASE ACF1 Training set -0.311974 1105.072 803.1194 -0.3683012 5.199148 0.7109852 -0.00255312 Can anyone show me how do I calculate the 'p value' and 't' statistic values for the various parameter estimates from the given standard errors? Best regards Deepak
multiply a vector of numbers with matrix rowwise
Consider a vector of numbers , a <- c(75,26,65,27,97,72) And a matrix 10x6 matrix b 1.4168709 0.6253624 2.08645202 2.9475645 1.29317931 0.80175442 0.3669328 0.851852 0.57428245 2.8542504 1.40075478 0.01745655 6.1173956 1.6848444 1.05468424 0.3382552 1.1428774 0.41141215 2.8203602 0.9573334 0.22131122 0.4406137 0.07209113 0.17910147 0.102152 0.1779387 0.94915127 0.3516491 1.48272109 0.06037996 0.3124434 0.4892484 2.04443039 0.1251463 2.41507973 1.25367433 0.2154152 0.3951161 0.60410084 0.7551265 0.55764737 1.17793564 1.5451135 0.7764766 3.11515773 1.3519765 0.08916275 1.39969422 0.4018092 0.2432501 0.06470464 2.6173665 0.24696145 5.27272096 1.1683212 0.1258633 0.19431636 0.4160356 1.61775945 0.78849181 dput b <- structure(c(1.41687091749774, 0.366932780481875, 6.11739562418232, 2.8203601760972, 0.102152034174651, 0.312443420290947, 0.215415194164962, 1.54511345728281, 0.401809234172106, 1.16832122397808, 0.625362366437912, 0.851851973640633, 1.68484436153414, 0.957333435262454, 0.177938693314666, 0.489248352590948, 0.395116138737649, 0.776476616387118, 0.243250062223524, 0.125863284132781, 2.08645202020619, 0.57428245106712, 1.05468423915856, 0.221311220899224, 0.949151266561806, 2.04443038991633, 0.604100843891501, 3.11515773070936, 0.0647046443940286, 0.194316359037562, 2.94756450172152, 2.85425036383753, 0.338255227074493, 0.440613748457464, 0.351649099495262, 0.125146273523569, 0.755126529331219, 1.35197646259786, 2.61736654663894, 0.416035552509129, 1.29317931454153, 1.40075477585735, 1.14287740174205, 0.072091125883162, 1.48272109049815, 2.41507973323081, 0.557647368015562, 0.0891627511009574, 0.246961451135576, 1.61775945491138, 0.80175441955164, 0.0174565480835137, 0.411412146408111, 0.179101474117488, 0.0603799588836676, 1.25367433010839, 1.17793564121695, 1.39969422101023, 5.27272095591089, 0.788491813423944), .Dim = c(10L, 6L)) My question is how do I multiply the vector a with matrix b, row wise. I know what b%*%a will do. I am trying to do something like this 75*1.4168709 + 26*0.6253624 + 65*2.08645202 + 27*2.9475645 + 97*1.29317931 + 72*0.80175442 75*0.3669328 + 26*0.851852 + 65*0.57428245 + 27*2.8542504 + 97*1.40075478 + 72*0.01745655 so on Any suggestions are much appreciated.
Looks like a sweep-operation. In R for functions applied to a marging, "2" generally indicates a column operation, which from your argument and structures is how I would describe your expected result. n(I can see how you would call this "row-wise" but most R users would think of this as being applied "column-wise:. > sweep(b,2,a,"*") [,1] [,2] [,3] [,4] [,5] [,6] [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318 [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871 [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675 [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306 [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357 [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552 [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366 [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984 [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909 [10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411 Then just rowSums: > rowSums( sweep(b,2,a,"*") ) [1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541 Alternatively, the matrix operation: a %*% t(b) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541 And the slightly faster single function version: tcrossprod(a,b) [,1] [,2] [,3] [,4] [,5] [,6] [,7] [,8] [,9] [,10] [1,] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541
We can get the lengths same before doing the multiplication i.e. by replicating the 'a' elements a[col(b)] * b # [,1] [,2] [,3] [,4] [,5] [,6] # [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318 # [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871 # [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675 # [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306 # [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357 # [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552 # [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366 # [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984 # [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909 #[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411 or transpose the 'b', then multiply with 'a' and transpose the output t(t(b) * a) # [,1] [,2] [,3] [,4] [,5] [,6] # [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318 # [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871 # [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675 # [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306 # [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357 # [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552 # [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366 # [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984 # [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909 #[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411 Or replicate more explicitly with rep rep(a, each = nrow(b)) * b # [,1] [,2] [,3] [,4] [,5] [,6] # [1,] 106.265319 16.259422 135.619381 79.584242 125.438394 57.726318 # [2,] 27.519959 22.148151 37.328359 77.064760 135.873213 1.256871 # [3,] 458.804672 43.805953 68.554476 9.132891 110.859108 29.621675 # [4,] 211.527013 24.890669 14.385229 11.896571 6.992839 12.895306 # [5,] 7.661403 4.626406 61.694832 9.494526 143.823946 4.347357 # [6,] 23.433257 12.720457 132.887975 3.378949 234.262734 90.264552 # [7,] 16.156140 10.273020 39.266555 20.388416 54.091795 84.811366 # [8,] 115.883509 20.188392 202.485252 36.503364 8.648787 100.777984 # [9,] 30.135693 6.324502 4.205802 70.668897 23.955261 379.635909 #[10,] 87.624092 3.272445 12.630563 11.232960 156.922667 56.771411 Or we could split the matrix 'b' by column into a list, and use that with mapply. Now, the corresponding individual units are multiplied mapply(`*`, split(b, col(b)), a) Once, we have completed the above step, just do rowSums out2 <- rowSums(a[col(b)] * b) out2 #[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541 -check the output with the OP's method out1 <- (b%*%a)[,1] out1 #[1] 520.8931 301.1913 720.7788 282.5876 231.6485 496.9479 224.9873 484.4873 514.9261 328.4541 all.equal(out1, out2) #[1] TRUE
How to do truncated SVD in R
I have two matrices, train and test. How do I "fit" a singular value decomposition on train and apply the fitted transformation to test? For example library(irlba) # train train <- cbind(matrix(runif(16, min=0, max=1), nrow=8), matrix(runif(16, min=30, max=31), nrow=8)) train[1:4, ] = train[1:4, ] + 50 # test test <- cbind(matrix(runif(16, min=0, max=1), nrow=8), matrix(runif(16, min=30, max=31), nrow=8)) test[1:4, ] = test[1:4, ] + 50 # trunacted SVD applied to train S <- irlba(t(train), nv=2) > train [,1] [,2] [,3] [,4] [1,] 50.39686 50.8733 80.57 80.51 [2,] 50.42719 50.2288 80.64 80.17 [3,] 50.87391 50.6059 80.19 80.61 [4,] 50.52439 50.7037 80.59 80.36 [5,] 0.43121 0.4681 30.93 30.76 [6,] 0.69381 0.5647 30.12 30.11 [7,] 0.02068 0.3382 30.37 30.04 [8,] 0.61101 0.5401 30.12 30.86 > S$v [,1] [,2] [1,] 0.4819 0.23134 [2,] 0.4805 0.18348 [3,] 0.4816 0.07372 [4,] 0.4816 -0.05819 [5,] 0.1370 -0.59769 [6,] 0.1342 -0.20746 [7,] 0.1335 -0.70946 [8,] 0.1358 -0.01972 Now, how do I reduce the dimensions of test? (Also, please note that my real datasets are large and sparse.)
Extract and store a specific position from multiple matrices in an array in R
Sorry, newbie...
I've got an array object called "y" of 500 matrices of 6x6, like this:
, , 1
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.0000 0.3627 0.4132 0.4231 0.3795 0.5444
[2,] 0.3627 0.0000 0.2084 0.3523 0.2310 0.5377
[3,] 0.4132 0.2084 0.0000 0.1984 0.2920 0.4774
[4,] 0.4231 0.3523 0.1984 0.0000 0.2787 0.4363
[5,] 0.3795 0.2310 0.2920 0.2787 0.0000 0.5129
[6,] 0.5444 0.5377 0.4774 0.4363 0.5129 0.0000
[...]
, , 500
[,1] [,2] [,3] [,4] [,5] [,6]
[1,] 0.0000 0.3755 0.3568 0.3835 0.3582 0.5065
[2,] 0.3755 0.0000 0.0840 0.2253 0.2237 0.4066
[3,] 0.3568 0.0840 0.0000 0.1673 0.2434 0.4073
[4,] 0.3835 0.2253 0.1673 0.0000 0.2338 0.3403
[5,] 0.3582 0.2237 0.2434 0.2338 0.0000 0.4263
[6,] 0.5065 0.4066 0.4073 0.3403 0.4263 0.0000
I want to extract a specific position through all the 500 matrices in the array and store this 500 values in a vector named "unouno" for further analyses
I'm trying to do this:
for (i in 1:dim(y)[[3]]){
unouno<-y[2,1,i, drop=F]
}
but it only extracts the value for the last (500th) matrix.
(Once solved this I want to extract and store separately the 500 values of each of the 6 x 6 positions in the matrices)
We can do this by leaving the 3rd dimension blank y[2,1,] data y <- array(1:60, dim=c(10,2,3))
If you would like to fix your loop, this could be one way to do it:
unouno <- NULL
for (i in 1:dim(y)[3]){
unouno[i]<-y[2,1,i]
}
It seems that you were mising indexing on the vector unouno as well