Calculate P values from Auto Arima model summary - r

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

Related

How to use & interpret bivariate GARCH GJR model using mGJR()

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.

error in computing the generalized eigenvalues in R with geigen package

I'm using the R package geigen to solve the generalized eigenvalue problem AV = lambdaB*V.
This is the code:
geigen(Gamma_chi_0, diag(diag(Gamma_xi_0)),symmetric=TRUE, only.values=FALSE) #GENERALIZED EIGENVALUE PROBLEM
Where:
Gamma_chi_0
[,1] [,2] [,3] [,4] [,5]
[1,] 1.02346 -0.50204 0.41122 -0.73066 0.00072
[2,] -0.50204 0.96712 -0.33526 0.51774 -0.37708
[3,] 0.41122 -0.33526 1.05086 0.09798 0.09274
[4,] -0.73066 0.51774 0.09798 0.99780 -0.51596
[5,] 0.00072 -0.37708 0.09274 -0.51596 1.03354
and
diag(diag(Gamma_xi_0))
[,1] [,2] [,3] [,4] [,5]
[1,] -0.0234 0.0000 0.0000 0.0000 0.0000
[2,] 0.0000 0.0329 0.0000 0.0000 0.0000
[3,] 0.0000 0.0000 -0.0509 0.0000 0.0000
[4,] 0.0000 0.0000 0.0000 0.0022 0.0000
[5,] 0.0000 0.0000 0.0000 0.0000 -0.0335
But I get this error:
> geigen(Gamma_chi_0, diag(diag(Gamma_xi_0)), only.values=FALSE)
Error in .sygv_Lapackerror(z$info, n) :
Leading minor of order 1 of B is not positive definite
In matlab, using the same two matrices, it works:
opt.disp = 0;
[P, D] = eigs(Gamma_chi_0, diag(diag(Gamma_xi_0)),r,'LM',opt);
% compute first r generalized eigenvectors and eigenvalues
For example I get the following eigenvalues matrix
D =
427.8208 0
0 -38.6419
Of course in matlab I just computed the first r=2, in R i want all the eigenvalues and eigenvectors (n=5), and then i subset the first 2.
Can someone help me to solve this?

geigen has detected a symmetric matrix for Gamma_chi_0. Then Lapack encounters an error and cannot continue. Specify symmetric=FALSE in the call of geigen. The manual describes what argument symmetric does. Do this
geigen(Gamma_chi_0, B, symmetric=FALSE, only.values=FALSE)
The result is (on my computer)
$values
[1] 4.312749e+02 -3.869203e+01 -2.328465e+01 1.706288e-05 1.840783e+01
$vectors
[,1] [,2] [,3] [,4] [,5]
[1,] -0.067535068 1.0000000 0.2249715 -0.89744514 0.05194799
[2,] -0.035746438 0.1094176 0.3273440 0.03714518 1.00000000
[3,] 0.005083806 0.3782606 0.8588086 0.50306323 0.17858115
[4,] -1.000000000 0.2986963 0.4067701 -1.00000000 -0.48314183
[5,] -0.034226056 -0.6075727 1.0000000 -0.53017872 0.06738515
$alpha
[1] 1.365959e+00 -1.152686e+00 -9.202769e-01 4.352770e-07 5.588102e-01
$beta
[1] 0.003167259 0.029791306 0.039522893 0.025510167 0.030357208
This is quite close to what you show for Matlab. I know nothing about Matlab so I cannot help you with that.
Addendum
Matlab seems to use similar methods as geigen when the matrices used are determined to be symmetric or not. Your matrix Gamma_chi_0 may not be exactly symmetric. See this documentation for argument 'algorithm' of eig.
More addendum
In actual fact your matrix B is not positive definite. Try the function chol of base R. And you'll get the same error message. In this case you have to force geigen to use the general algorithm.

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

How to deal with log of zero in R in image.plot?

I have a matrix, and the entries are all probabilities. Most of the entries have very low probabilities. Some have zeros. I need to do log of the matrix. However, since there are zeros in the matrix, R generates -inf for those zero entries. My goal is to feed this log(matrix) into the image.plot(). When I feed this into the image.plot, I kept getting this error:
Error in seq.default(minz + binwidth/2, maxz - binwidth/2, by = binwidth) :
invalid (to - from)/by in seq(.)
Is there any solution in here that can help me get around this?
Here is what the matrix looks like:
0 1 2 3 4 5 6
[1,] -0.0007854138 -8.9132811 -10.011893 -10.705041 -9.606428 -9.318746 -Inf
[2,] -0.3402118357 -1.6137090 -2.742625 -4.215836 -5.721434 -7.121522 -9.606428
[3,] -0.2912175507 -2.0296478 -3.521929 -4.275321 -4.426519 -4.187369 -3.715705
[4,] -1.5244380532 -0.7048802 -2.001368 -3.405243 -3.713864 -3.143919 -3.781412
[5,] -0.7572491288 -0.7487709 -3.981208 -5.110329 -5.228577 -5.095569 -5.293395
[6,] -0.0007629648 -Inf -8.759130 -7.613998 -9.606428 -Inf -Inf
[7,] -0.0020658381 -7.4861648 -7.526987 -7.094123 -9.318746 -Inf -Inf
[8,] -0.0295715883 -6.7160566 -7.208533 -6.610696 -6.485533 -6.813220 -6.387552
[9,] -0.0032128722 -6.7160566 -7.613998 -7.871827 -7.760602 -8.759130 -8.759130
[10,] -0.4869248130 -1.3225132 -2.518576 -3.768698 -5.140520 -6.183252 -7.208533
7 8 9
[1,] -Inf -10.705041 -10.011893
[2,] -Inf -Inf -7.149693
[3,] -4.965248 -5.968842 -6.428374
[4,] -4.696227 -5.091913 -4.669559
[5,] -5.163777 -5.468599 -6.577906
[6,] -Inf -Inf -Inf
[7,] -Inf -Inf -Inf
[8,] -6.627503 -6.456545 -6.400976
[9,] -10.011893 -10.011893 -Inf
[10,] -8.402456 -7.814669 -6.546158
Here is the structure :
structure(c(0.999214894571557, 0.71161956034096, 0.747353073126963,
0.217743382682817, 0.468954688200987, 0.999237326155227, 0.997936294302378,
0.970861372812921, 0.996792283535218, 0.614513234634365, 0.000134589502018843,
0.199147599820547, 0.13138178555406, 0.49416778824585, 0.472947510094213,
0, 0.000560789591745177, 0.00121130551816958, 0.00121130551816958,
0.266464782413638, 4.48631673396142e-05, 0.0644010767160162,
0.0295423956931359, 0.135150291610588, 0.0186630776132795, 0.00015702108568865,
0.00053835800807537, 0.000740242261103634, 0.000493494840735756,
0.0805742485419471, 2.24315836698071e-05, 0.0147599820547331,
0.0139075818752804, 0.0331987438313145, 0.00603409600717811,
0.000493494840735756, 0.000829968595782862, 0.00134589502018843,
0.000381336922386721, 0.0230820995962315, 6.72947510094213e-05,
0.00327501121579183, 0.0119560340960072, 0.0243831314490803,
0.00536114849708389, 6.72947510094213e-05, 8.97263346792284e-05,
0.00152534768954688, 0.000426200089726335, 0.00585464333781965,
8.97263346792284e-05, 0.000807537012113055, 0.0151861821444594,
0.0431135038133692, 0.00612382234185734, 0, 0, 0.00109914759982055,
0.00015702108568865, 0.00206370569762225, 0, 6.72947510094213e-05,
0.0243382682817407, 0.022790489008524, 0.00502467474203679, 0,
0, 0.00168236877523553, 0.00015702108568865, 0.000740242261103634,
0, 0, 0.00697622252131, 0.00912965455361149, 0.00572005383580081,
0, 0, 0.00132346343651862, 4.48631673396142e-05, 0.000224315836698071,
2.24315836698071e-05, 0, 0.00255720053835801, 0.00614625392552714,
0.00421713772992373, 0, 0, 0.0015702108568865, 4.48631673396142e-05,
0.000403768506056528, 4.48631673396142e-05, 0.000785105428443248,
0.00161507402422611, 0.00937640197397936, 0.00139075818752804,
0, 0, 0.00165993719156572, 0, 0.00143562135486765), .Dim = c(10L,
10L), .Dimnames = list(NULL, c("0", "1", "2", "3", "4", "5",
"6", "7", "8", "9")))

If these zeros are caused by a physical measurement which should yield a positive-definite results but fails to do so for technical reasons, it might be reasonable to substitute 1/2 of the lower limit of detection for the zeros.
M2 <- M
print( min(M[M!=0]), digits=16)
#[1] 2.24315836698071e-05
M2[M2==0] <- 0.5*min(M[M!=0])
image(M2)
image(log(M2))

True, a log plot may make "the difference betweeen entries more noticeable". However, if you have zeros in your data, you'd be using it wrong. The point of a logarithmic scale is to illustrate exponential increases in the data. Having zeros, however, means that either:
the values observed were not produced by a process exhibiting exponential
growth or
you need to handle your missing values differently.
Either way, what would work a lot better in your case is taking the square root of the values. Or (n>2)-th root if you want to accentuate the difference in values even more -- the higher the n, the bigger the difference.
As per #flodel's suggestion below, the code that would do this is: image.plot(sqrt(x)) or, more generally, image.plot(x^(1/n)) for some n>1.
Hope this helps.

A simple trick is to add 1 since log1=0 such that cell with 0 still will have 0 after log transformation.
k<-matrix(c(1:8,0,0),nrow=2,ncol=5)
> k
[,1] [,2] [,3] [,4] [,5]
[1,] 1 3 5 7 0
[2,] 2 4 6 8 0
log(k)
[,1] [,2] [,3] [,4] [,5]
[1,] 0.0000000 1.098612 1.609438 1.945910 -Inf
[2,] 0.6931472 1.386294 1.791759 2.079442 -Inf
log(k+1)
[,1] [,2] [,3] [,4] [,5]
[1,] 0.6931472 1.386294 1.791759 2.079442 0
[2,] 1.0986123 1.609438 1.945910 2.197225 0

The except is thrown by seq(), which can not take -inf as any one of its arguments. You can get exactly the same type of error with the following code:
> seq(-log(0), 0, 50)
Error in seq.default(-log(0), 0, 50) : invalid (to - from)/by in seq(.)
To avoid it, follow #Metrics 's trick. Although I will suggest instead of adding 1.0, add a very small value, such as 1e-22, since your matrix is a matrix of probabilities.

Can't paste multiple lines of code in a comment, but this example shows what I meant:
> m=cbind(c(0,0.88,0.99),c(1,2,1),c(3,4,5))
> m=as.matrix(m)
> log(m)
[,1] [,2] [,3]
[1,] -Inf 0.0000000 1.098612
[2,] -0.12783337 0.6931472 1.386294
[3,] -0.01005034 0.0000000 1.609438
> m
[,1] [,2] [,3]
[1,] 0.00 1 3
[2,] 0.88 2 4
[3,] 0.99 1 5

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