[时间序列问题] arch拟合只有1阶滞后显著，还可以用garch模型吗？ [推广有奖]

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奔跑的小夏夏 发表于 2020-2-5 19:17:10 |AI写论文

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对OLS残差是否存在arch效应进行LM检验得到下列结果：
LM test for autoregressive conditional heteroskedasticity (ARCH)
---------------------------------------------------------------------------
lags(p)  |       chi2             df                Prob > chi2
-------------+-------------------------------------------------------------
   1    |       4.066             1                0.0438
   2    |       4.239             2                0.1201
   3    |       4.086             3                0.2523
   4    |       4.118             4                0.3903
   5    |       7.459             5                0.1887
---------------------------------------------------------------------------

      H0: no ARCH effects    vs.  H1: ARCH(p) disturbance
只有1阶滞后显著，可以用garch（1,1）拟合吗？
如果拟合后，结果是这样：
*拟合garch(1,1)模型
. arch d_ln_reer L(1/1).d_ln_reer,arch(1) garch(1)

(setting optimization to BHHH)
Iteration 0: log likelihood =  305.21625
Iteration 1: log likelihood =  307.17998
Iteration 2: log likelihood =  309.08408
Iteration 3: log likelihood = 309.3325
Iteration 4: log likelihood = 309.4862
(switching optimization to BFGS)
Iteration 5: log likelihood =  309.58782
Iteration 6: log likelihood =  309.60984
BFGS stepping has contracted, resetting BFGS Hessian (0)
Iteration 7: log likelihood = 309.6135
Iteration 8: log likelihood = 309.6135  (backed up)
Iteration 9: log likelihood =  309.61351  (backed up)
Iteration 10:  log likelihood =  309.61354  (backed up)
Iteration 11:  log likelihood =  309.61359  (backed up)
Iteration 12:  log likelihood = 309.6136
Iteration 13:  log likelihood =  309.61365
Iteration 14:  log likelihood =  309.61365

ARCH family regression

Sample: 3 - 108                                  Number of obs =       106
Distribution: Gaussian                         Wald chi2(1) =    12.06
Log likelihood =  309.6136                      Prob > chi2    =    0.0005

------------------------------------------------------------------------------
         |                OPG
d_ln_reer |    Coef. Std. Err.    z P>|z|    [95% Conf. Interval]
-------------+----------------------------------------------------------------
d_ln_reer |
d_ln_reer |
      L1. | .3115586 .0897115    3.47 0.001    .1357273    .48739
         |
   _cons | .0022409 .0014538    1.54 0.123 -.0006084 .0050902
-------------+----------------------------------------------------------------
ARCH       |
      arch |
      L1. | .0909432 .0883142    1.03 0.303 -.0821494 .2640358
         |
   garch |
      L1. | .8313638 .1690913    4.92 0.000    .499951 1.162777
         |
   _cons | .0000134 .0000189    0.71 0.478 -.0000236 .0000504
------------------------------------------------------------------------------

. *检验arch项和garch项联合显著
. test [ARCH]L1.arch [ARCH]L1.garch

( 1)  [ARCH]L.arch = 0
( 2)  [ARCH]L.garch = 0

         chi2(  2) = 81.87
      Prob > chi2 = 0.0000