garch.m

对GARCH－t模型参数的估计,主要是运用已有的股票数据估计参数

Rhf =[-2.4589     %哈飞股票的收益率矩阵，253个数据
    3.1504
   -2.0892
   -1.7750
   -5.2199
    2.6072
         0
   -2.2306
   -3.9100
   -2.5338
    4.0084
   -1.4746
   -1.3381
    1.1032
   -2.1387
    0.0800
    0.7968
   -2.0851
   -5.1549
    1.5242
    0.1679
    0.5021
    2.6361
    4.8403
   -1.2471
   -1.1834
   -2.0041
    0.5652
    5.4067
   -2.3930
    1.0878
    2.8192
    1.1949
    0.9605
   -1.1091
   -4.0203
   -2.0329
   -5.0213
    2.2178
   -0.9796
   -0.3287
    2.9998
    0.7955
    3.5801
   -0.2296
    5.5880
   -3.1655
   -3.3463
    0.6936
   -1.7041
   -1.9725
   -0.9608
    1.6753
   -0.4758
    3.7446
    5.4390
   -0.4360
    3.9277
   -2.5533
   -5.0840
    6.2978
    7.5830
   -4.3704
         0
    4.2388
    9.5430
    4.0487
   -3.3921
   -3.2651
   -2.6153
    2.1224
   -1.0556
  -10.3836
   -2.4537
    0.4249
    9.5631
    5.7408
    5.3141
   -2.9766
    4.7435
   -2.6332
   -1.8736
    0.8826
    6.0797
    1.4231
   -7.9137
    2.3257
   -6.8993
    4.5736
    7.3688
   -0.9885
    0.7149
    3.8166
   -3.5977
   -2.3791
    2.0505
   -2.3308
    0.3363
   -1.9780
    9.5206
    0.1037
   -0.4677
    0.8815
   -2.1394
    4.1328
   -2.3037
   -3.2100
   -2.2169
    1.6269
    0.9103
    0.3724
   -0.1063
   -1.1227
    1.6529
    2.2485
    2.1990
   -2.5616
    0.5176
    3.3006
    1.3396
   -0.7420
    1.9666
   -1.5208
    7.8863
    1.2259
   -1.8675
   -1.1561
   -3.6471
    5.9461
   -1.0510
   -1.9013
   -0.1405
    0.2341
    2.5400
    2.9652
    0.3976
    1.0526
    5.5169
   -3.3161
    0.1706
   -2.9401
    2.9401
    0.2553
   -0.3406
  -10.5124
   -6.4570
   -2.6108
   -1.4629
    3.4656
   -1.5886
   -1.2474
    2.2752
    4.1558
   -2.7344
   -1.5236
    2.2268
    0.0500
   -1.5121
   -3.5146
   -4.9053
    9.5310
    1.8906
    2.4344
  -10.5414
   -2.1611
   -0.3830
   -2.6105
  -10.5548
    5.2980
    2.4027
   -6.5813
    0.5550
    0.1843
   -0.0614
    3.2631
   -1.3166
    1.7911
    2.8006
    3.3940
   -1.1186
    2.6639
    0.1642
   -0.7684
    2.1799
   -8.3733
    3.0594
   -0.2277
    4.1301
    2.2704
    8.2055
   -2.6948
   -5.0309
    2.0011
   -3.0706
    0.3221
   -0.9152
    2.5101
    3.4218
   -1.2824
    1.7401
    2.4061
    3.8382
   -5.2347
   -0.3522
    1.5008
   -2.2597
    0.7085
   -1.9349
   -2.0255
    0.7839
    0.8811
    4.3913
   -3.4157
   -1.4411
   -0.5719
    3.0298
    5.9404
   -2.6565
   -2.8297
    6.3877
   -2.9724
    3.8659
   -2.9938
   -2.6394
   -3.8369
    2.4404
   -2.9047
    2.3506
   -4.2296
   -0.4753
   -3.9962
   -1.6107
    0.1678
   -9.9848
   -3.0733
    1.0770
    7.2306
   -1.6549
    0.1191
    3.6240
   -0.6912
   -2.9923
   -4.6946
   -0.8148
   -2.3560
    0.6423
    3.5842
   -2.4384
    9.5310
    9.5415
    1.3507
   -0.8811
    9.5263];
Rsyhg =[0.1771   %沈阳化工股票的收益率，调整之后跟哈飞股票数据数目相同
    3.8199
   -0.6838
    5.5060
   -1.9673
    1.8048
   -2.8032
   -1.6864
   -3.2847
   -0.1759
    1.5721
         0
   -1.2206
   -1.4135
   -2.1584
    0.1817
    0.3623
   -4.8157
   -4.2642
    2.3484
    0.3861
   -0.9681
    2.1175
   -1.7291
    3.4289
   -0.9407
   -0.5687
    1.8833
    0.7435
   -1.3048
   -1.1321
    3.5418
   -1.8485
    3.4834
    0.1800
   -1.8149
         0
   -1.8485
    2.0315
    3.9432
   -0.1759
    2.7780
    1.6978
   -0.1685
   -1.1875
    1.3560
   -2.2129
   -1.9114
         0
    1.9114
   -2.9697
   -3.9788
    0.9183
    1.4519
    3.5402
    4.5887
   -1.0017
    5.3891
         0
    1.1067
    5.2079
    0.4468
   -6.1275
    5.5314
    4.5296
    4.0593
   -0.6882
   -1.2509
   -7.7017
    3.8523
    5.6512
    4.0382
   -6.1202
    4.1215
   -4.2618
    0.9783
    3.0139
    3.1875
    0.6515
    2.3108
    2.6301
         0
    1.1063
    1.5767
   -0.3617
  -10.1610
    5.8420
   -4.3821
    0.1317
    1.4370
    0.2591
    2.6804
    2.8556
   -2.3530
    0.8734
    2.0898
   -3.3398
    2.2389
   -2.4908
    0.8789
    2.4693
    4.4134
   -1.6471
   -0.9535
    8.0503
   -0.5540
   -2.9314
   -4.0870
    0.4756
    2.9225
    2.5030
    3.5324
   -0.8715
    0.1093
    1.3030
   -2.7339
    5.2900
    1.9782
    1.5346
    2.0101
   -0.6990
    1.6891
   -7.6764
    9.5310
    5.3660
    5.1797
   -2.1109
    3.4079
    2.7120
    4.4961
    3.8421
    1.8293
   -2.4466
   -3.9468
    8.3382
    3.6368
    2.8171
    4.8790
   -0.8635
    0.3330
   -4.8358
    2.4131
    7.8574
   -0.1891
  -10.5010
    0.9069
  -12.1697
    0.1567
    9.4099
    0.0713
    0.9922
    1.5396
    3.2790
   -0.5391
    0.0675
    3.7115
   -1.5738
   -3.5658
   -2.4265
   -3.8631
  -10.4469
    4.7440
   -7.6189
   -6.1875
    0.1771
         0
    4.2449
   -8.0325
    6.9238
    3.2900
   -6.2494
   -0.3540
    0.8826
   -4.6771
   -5.9762
   -1.7752
   -0.3988
    6.4788
    6.2605
   -1.9539
    3.9566
    0.8584
   -0.5141
    7.1281
  -10.5361
    3.8366
    2.6173
    3.3596
   -2.0351
    6.9103
    1.4476
   -5.7603
    4.9248
    0.7599
    1.8748
    2.1316
    3.9221
    6.3664
   -0.9891
   -2.0081
   -0.0676
    9.5433
   -3.7598
    2.7088
   -0.9994
   -5.2186
    9.5190
    8.4704
   -7.2155
   -3.5049
   -1.9249
    0.2505
   -3.1124
    1.5365
    3.8634
   -4.8851
   -3.2619
    0.2649
   -5.5759
    2.4181
    0.2046
   -0.8895
    0.6849
   -4.1106
   -4.4355
    2.8584
    3.1297
    3.0347
   -5.4445
    0.6435
   -5.3434
   -4.6950
   -4.3485
  -10.4903
   -1.2880
    3.0996
    8.9253
   -5.4843
   -4.7057
    1.7125
    1.8593
    1.7392
   -6.2242
    0.8223
   -5.6142
    0.7670
    6.2925
   -3.4675
   -0.7456
    3.6735
   -0.2709
   -5.5777
    2.6417];
uhf=0.151293;
a1=Rhf-uhf;            %按哈飞股票收益率算出的GARCH模型里的a(t)
alpha01=0.965410;      %按哈飞股票收益率算出的GARCH模型里的alpha0
alpha11=0.047787;      %按哈飞股票收益率算出的GARCH模型里的alpha1
beta1=0.886927;        %按哈飞股票收益率算出的GARCH模型里的beta
for t=2:253
    sigma1(1)=100*a1(1);   %相当于给epsilon赋初值0.01（初值不知道赋什么值合适）
    sigma1(t)=sqrt(alpha01+alpha11*(a1(t-1))^2+beta1*(sigma1(t-1))^2);
epsilon1(t)=a1(t)/sigma1(t);     
u1(t)=tpdf(epsilon1(t),7.781719);  %边缘分布
end
u1(1)=tpdf(0.01,7.781719); 
usyhg=0.254581;     %意义同上
a2=Rsyhg-usyhg;
alpha02=-0.005624;
alpha12=-0.007702;
beta2=1.013234;
for t=2:253
   sigma2(1)=100*a2(1);
   sigma2(t)=sqrt(alpha02+alpha12*(a2(t-1))^2+beta2*(sigma2(t-1))^2);
epsilon2(t)=a2(t)/sigma2(t);
u2(t)=tpdf(epsilon2(t),70.94758);
end
u2(1)=tpdf(0.01,70.94758);
u1;
u2;
 for t=1:252
     if  0<u1(t)<1
ksai1(t)=norminv(u1(t),0,1);
     else
         t=t+1;ksai1(t)=norminv(u1(t),0,1);
     end
 end
for t=1:252
    if 0<u2(t)<1
ksai2(t)=norminv(u2(t),0,1); 
    else
      t=t+1;ksai2(t)=norminv(u2(t),0,1);  
    end     
end
for t=1:253
ksai(t,:)=[ksai1(t)  ksai2(t)];   %？
end
for t=1:253
s=(ksai(t,:))'*ksai(t,:);
while t<253
    t=t+1;
s=s+(ksai(t-1,:))'*ksai(t-1,:);
end
end
s;
    bigsigma=s/253;   %为了估计t-copula的∑，给出∑的初值    
for t=(1:253)
    zeta1(t)=tinv(u1(t),3);zeta2(t)=tinv(u2(t),3);   %取t-copula的自由度为3,估计∑的值
    zeta(t,:)=[zeta1(t) zeta2(t)];
end
for i=1:5
for t=(1:253)
  w=((zeta(t,:))'*zeta(t,:))/(1+zeta(t,:)*bigsigma*(zeta(t,:))'/3);
  while t<253
   t=t+1;
   w=w+((zeta(t-1,:))'*zeta(t-1,:))/(1+zeta(t-1,:)*bigsigma*(zeta(t-1,:))'/3);
  end
 end
w;
  bigsigma=5*w/(253*3);         
end
bigsigma