[1] "NOBS="
[1] 1996
iteration = 0
Step:
[1] 0 0 0
Parameter:
[1] 0.001 0.001 0.001
Function Value
[1] 934247
Gradient:
[1]    -118588.2 -699156429.8 -238500419.5

iteration = 1
Step:
[1] 0.01605326 0.94644626 0.32285740
Parameter:
[1] 0.01705326 0.94744626 0.32385740
Function Value
[1] 3335.237
Gradient:
[1]  -90.4743 -230.2289 -123.0296

iteration = 2
Step:
[1] 0.0000122474921 0.0000003116618 0.0000001665454
Parameter:
[1] 0.01706550 0.94744657 0.32385757
Function Value
[1] 3335.235
Gradient:
[1]  -90.45172 -230.22679 -123.03074

iteration = 3
Step:
[1] 0.0530520855 0.0013503405 0.0007216065
Parameter:
[1] 0.07011759 0.94879691 0.32457918
Function Value
[1] 3332.64
Gradient:
[1]    7.571266 -223.159244 -127.903126

iteration = 4
Step:
[1] -0.0000818879225 -0.0000017566372 -0.0000009270364
Parameter:
[1] 0.0700357 0.9487952 0.3245782
Function Value
[1] 3332.64
Gradient:
[1]    7.419894 -223.166429 -127.894927

iteration = 5
Step:
[1] -0.000640683385 -0.000010853360 -0.000005605306
Parameter:
[1] 0.06939502 0.94878430 0.32457264
Function Value
[1] 3332.639
Gradient:
[1]    6.235563 -223.218796 -127.827457

iteration = 6
Step:
[1] -0.000722522825 -0.000006090759 -0.000002815952
Parameter:
[1] 0.0686725 0.9487782 0.3245698
Function Value
[1] 3332.636
Gradient:
[1]    4.899868 -223.269497 -127.744068

iteration = 7
Step:
[1] -0.001363021615  0.000006256053  0.000004804330
Parameter:
[1] 0.06730947 0.94878447 0.32457463
Function Value
[1] 3332.629
Gradient:
[1]    2.379936 -223.341141 -127.565849

iteration = 8
Step:
[1] -0.00208419894  0.00005444748  0.00003293185
Parameter:
[1] 0.06522528 0.94883891 0.32460756
Function Value
[1] 3332.612
Gradient:
[1]   -1.473311 -223.389727 -127.240209

iteration = 9
Step:
[1] -0.0034394223  0.0002088667  0.0001221925
Parameter:
[1] 0.06178585 0.94904778 0.32472976
Function Value
[1] 3332.566
Gradient:
[1]   -7.830936 -223.308615 -126.562972

iteration = 10
Step:
[1] -0.0054846392  0.0006426573  0.0003713410
Parameter:
[1] 0.05630121 0.94969044 0.32510110
Function Value
[1] 3332.446
Gradient:
[1]  -17.96032 -222.76006 -125.12184

iteration = 11
Step:
[1] -0.008745857  0.001834771  0.001053890
Parameter:
[1] 0.04755536 0.95152521 0.32615499
Function Value
[1] 3332.137
Gradient:
[1]  -34.0670 -220.7953 -121.8959

iteration = 12
Step:
[1] -0.013462126  0.004931735  0.002823657
Parameter:
[1] 0.03409323 0.95645694 0.32897865
Function Value
[1] 3331.353
Gradient:
[1]  -58.6543 -214.9863 -114.6135

iteration = 13
Step:
[1] -0.019115769  0.012463378  0.007122344
Parameter:
[1] 0.01497746 0.96892032 0.33610099
Function Value
[1] 3329.459
Gradient:
[1]  -92.77922 -199.85287  -98.78506

iteration = 14
Step:
[1] -0.02166991  0.02819428  0.01609234
Parameter:
[1] -0.006692443  0.997114600  0.352193333
Function Value
[1] 3325.369
Gradient:
[1] -129.12524 -166.55093  -68.78893

iteration = 15
Step:
[1] -0.01103468  0.05165017  0.02945412
Parameter:
[1] -0.01772712  1.04876477  0.38164745
Function Value
[1] 3318.377
Gradient:
[1] -142.96556 -111.16762  -26.13048

iteration = 16
Step:
[1] 0.01779693 0.06500385 0.03704038
Parameter:
[1] 0.00006981359 1.11376862004 0.41868783305
Function Value
[1] 3310.725
Gradient:
[1] -107.69713  -51.49116   12.26802

iteration = 17
Step:
[1] 0.03682847 0.04305453 0.02451046
Parameter:
[1] 0.03689828 1.15682315 0.44319829
Function Value
[1] 3306.973
Gradient:
[1] -46.25360 -17.28797  30.37897

iteration = 18
Step:
[1] 0.021984063 0.007922206 0.004496142
Parameter:
[1] 0.05888235 1.16474536 0.44769444
Function Value
[1] 3306.372
Gradient:
[1] -11.23299 -10.83824  32.35184

iteration = 19
Step:
[1]  0.006211854 -0.003984563 -0.002277181
Parameter:
[1] 0.0650942 1.1607608 0.4454173
Function Value
[1] 3306.309
Gradient:
[1]  -1.429653 -13.096709  30.214165

iteration = 20
Step:
[1]  0.001259474 -0.003781783 -0.002157089
Parameter:
[1] 0.06635367 1.15697901 0.44326017
Function Value
[1] 3306.299
Gradient:
[1]   0.5498136 -15.4933834  28.4594874

iteration = 21
Step:
[1] -0.0002511085 -0.0007659533 -0.0004364756
Parameter:
[1] 0.06610257 1.15621306 0.44282369
Function Value
[1] 3306.299
Gradient:
[1]   0.1466760 -16.0045622  28.1342978

iteration = 22
Step:
[1] -0.00007290668 -0.00004110206 -0.00002341991
Parameter:
[1] 0.06602966 1.15617196 0.44280027
Function Value
[1] 3306.299
Gradient:
[1]   0.03050445 -16.03459643  28.12077442

iteration = 23
Step:
[1] -0.000014025051 -0.000003308249 -0.000001940183
Parameter:
[1] 0.06601563 1.15616865 0.44279833
Function Value
[1] 3306.299
Gradient:
[1]   0.00818136 -16.03736253  28.12020956

iteration = 24
Step:
[1] -0.000070277355 -0.000015656154 -0.000009540787
Parameter:
[1] 0.06594536 1.15615299 0.44278879
Function Value
[1] 3306.299
Gradient:
[1]  -0.1036606 -16.0507715  28.1176256

iteration = 25
Step:
[1] -0.00008416019 -0.00001810554 -0.00001181497
Parameter:
[1] 0.0658612 1.1561349 0.4427770
Function Value
[1] 3306.299
Gradient:
[1]  -0.2375373 -16.0665608  28.1144968

iteration = 26
Step:
[1] -0.00015466750 -0.00003217741 -0.00002323349
Parameter:
[1] 0.06570653 1.15610271 0.44275374
Function Value
[1] 3306.298
Gradient:
[1]  -0.4834224 -16.0953591  28.1083603

iteration = 27
Step:
[1] -0.00023907198 -0.00004689140 -0.00003974482
Parameter:
[1] 0.06546746 1.15605582 0.44271400
Function Value
[1] 3306.298
Gradient:
[1]  -0.8631514 -16.1391869  28.0979063

iteration = 28
Step:
[1] -0.00039432877 -0.00007006723 -0.00007583606
Parameter:
[1] 0.06507313 1.15598575 0.44263816
Function Value
[1] 3306.298
Gradient:
[1]  -1.488478 -16.209932  28.077929

iteration = 29
Step:
[1] -0.00063487446 -0.00009346531 -0.00014862164
Parameter:
[1] 0.06443825 1.15589229 0.44248954
Function Value
[1] 3306.296
Gradient:
[1]  -2.49278 -16.31945  28.03887

iteration = 30
Step:
[1] -0.0010315614 -0.0001016240 -0.0003110489
Parameter:
[1] 0.06340669 1.15579066 0.44217849
Function Value
[1] 3306.293
Gradient:
[1]  -4.117771 -16.486233  27.957156

iteration = 31
Step:
[1] -0.00166861600 -0.00003311419 -0.00068413739
Parameter:
[1] 0.06173808 1.15575755 0.44149435
Function Value
[1] 3306.283
Gradient:
[1]  -6.72815 -16.72658  27.77750

iteration = 32
Step:
[1] -0.0026854091  0.0002879379 -0.0015713764
Parameter:
[1] 0.05905267 1.15604549 0.43992298
Function Value
[1] 3306.259
Gradient:
[1] -10.87969 -17.03692  27.36317

iteration = 33
Step:
[1] -0.004233081  0.001339505 -0.003689981
Parameter:
[1] 0.05481959 1.15738499 0.43623299
Function Value
[1] 3306.196
Gradient:
[1] -17.28641 -17.32708  26.37859

iteration = 34
Step:
[1] -0.006272579  0.004270862 -0.008555941
Parameter:
[1] 0.04854701 1.16165585 0.42767705
Function Value
[1] 3306.044
Gradient:
[1] -26.39276 -17.24529  24.02295

iteration = 35
Step:
[1] -0.007687224  0.011089085 -0.018139888
Parameter:
[1] 0.04085978 1.17274494 0.40953717
Function Value
[1] 3305.714
Gradient:
[1] -36.49098 -15.84974  18.65346

iteration = 36
Step:
[1] -0.004599669  0.021585431 -0.029247559
Parameter:
[1] 0.03626011 1.19433037 0.38028961
Function Value
[1] 3305.188
Gradient:
[1] -39.930771 -11.687772   8.813616

iteration = 37
Step:
[1]  0.005318178  0.024606984 -0.024621730
Parameter:
[1] 0.04157829 1.21893735 0.35566788
Function Value
[1] 3304.696
Gradient:
[1] -28.1559510  -5.0166889  -0.3709907

iteration = 38
Step:
[1]  0.011776486  0.012246202 -0.004756662
Parameter:
[1] 0.05335478 1.23118355 0.35091122
Function Value
[1] 3304.451
Gradient:
[1] -9.2553942  0.2620565 -1.4901267

iteration = 39
Step:
[1]  0.005889702 -0.001650089  0.003493281
Parameter:
[1] 0.05924448 1.22953346 0.35440450
Function Value
[1] 3304.418
Gradient:
[1] -0.7236886  0.5688100 -0.1758467

iteration = 40
Step:
[1]  0.0005983181 -0.0015382102  0.0008996235
Parameter:
[1] 0.0598428 1.2279953 0.3553041
Function Value
[1] 3304.418
Gradient:
[1]  0.04475260  0.08429264 -0.02794622

iteration = 41
Step:
[1] -0.00000999935 -0.00023893597  0.00013481951
Parameter:
[1] 0.0598328 1.2277563 0.3554389
Function Value
[1] 3304.418
Gradient:
[1] 0.0087011358 0.0037216680 0.0007714761

iteration = 42
Parameter:
[1] 0.05982754 1.22774823 0.35544002
Function Value
[1] 3304.418
Gradient:
[1]  0.000334239303 -0.000026668179  0.000003838178

Relative gradient close to zero.
Current iterate is probably solution.

$minimum
[1] 3304.418

$estimate
[1] 0.05982754 1.22774823 0.35544002

$gradient
[1]  0.000334239303 -0.000026668179  0.000003838178

$hessian
           [,1]      [,2]      [,3]
[1,] 1515.36196  37.92259 -87.66961
[2,]   37.92259 470.79763 239.50411
[3,]  -87.66961 239.50411 630.74982

$code
[1] 1

$iterations
[1] 42

           [,1]       [,2]
[1,] 0.05982754 0.02590790
[2,] 1.22774823 0.05153810
[3,] 0.35544002 0.04466137

LB tests on z and z^2

	Box-Ljung test

data:  z 
X-squared = 7.8088, df = 1, p-value = 0.005199


	Box-Ljung test

data:  z 
X-squared = 36.319, df = 10, p-value = 0.00007418


	Box-Ljung test

data:  z2 
X-squared = 1.0696, df = 1, p-value = 0.3010


	Box-Ljung test

data:  z2 
X-squared = 301.2573, df = 10, p-value < 0.00000000000000022


LB tests on returns^2

	Box-Ljung test

data:  y^2 
X-squared = 50.0429, df = 1, p-value = 0.000000000001504

 = 301.2573, df = 10, p-value < 0.00000000000000022


LB tests on returns^2

	Box-Ljung test

data:  y^2 
X-squared = 50.0429, df = 1, p-value = 0.000000000001504