ARMA(1,2)-EGARCH(2,1)杠杆解释

Question

我从统计开始，我面临一个ARMA模型的问题。

我对从ARMA(1,2)-eGARCH(2,1)的拟合来解释伽马系数有问题。

我知道伽马参数是杠杆，当伽马是负的，它意味着模型有杠杆效应，但问题是在这个模型中，我有两个伽马参数，一个是负的，另一个是正的。

我怎么解释这个案子？

这是适合的模型。

谢谢你的帮忙!

*---------------------------------*
*          GARCH Model Fit        *
*---------------------------------*

Conditional Variance Dynamics   
-----------------------------------
GARCH Model : eGARCH(2,1)
Mean Model  : ARFIMA(1,0,2)
Distribution    : std 

Optimal Parameters
------------------------------------
        Estimate  Std. Error     t value Pr(>|t|)
mu      0.002335    0.000586  3.9845e+00 0.000068
ar1     0.984861    0.004176  2.3583e+02 0.000000
ma1    -1.039860    0.000004 -2.6259e+05 0.000000
ma2     0.062858    0.002236  2.8106e+01 0.000000
omega  -0.027390    0.009831 -2.7860e+00 0.005336
alpha1 -0.036038    0.048493 -7.4316e-01 0.457383
alpha2  0.092501    0.048862  1.8931e+00 0.058344
beta1   0.995196    0.001996  4.9852e+02 0.000000
gamma1  0.345047    0.061117  5.6457e+00 0.000000
gamma2 -0.093125    0.058722 -1.5859e+00 0.112770
shape   2.533085    0.146629  1.7276e+01 0.000000

Robust Standard Errors:
        Estimate  Std. Error     t value Pr(>|t|)
mu      0.002335    0.000570  4.1000e+00 0.000041
ar1     0.984861    0.004516  2.1809e+02 0.000000
ma1    -1.039860    0.000003 -4.0642e+05 0.000000
ma2     0.062858    0.002186  2.8754e+01 0.000000
omega  -0.027390    0.015389 -1.7799e+00 0.075091
alpha1 -0.036038    0.048691 -7.4014e-01 0.459217
alpha2  0.092501    0.047530  1.9462e+00 0.051636
beta1   0.995196    0.002408  4.1322e+02 0.000000
gamma1  0.345047    0.058689  5.8792e+00 0.000000
gamma2 -0.093125    0.057076 -1.6316e+00 0.102767
shape   2.533085    0.150352  1.6848e+01 0.000000

LogLikelihood : 5007.332 

Information Criteria
------------------------------------
                
Akaike       -4.1004
Bayes        -4.0742
Shibata      -4.1004
Hannan-Quinn -4.0909

Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
                         statistic   p-value
Lag[1]                       13.66 2.196e-04
Lag[2*(p+q)+(p+q)-1][8]      21.16 0.000e+00
Lag[4*(p+q)+(p+q)-1][14]     27.59 7.616e-10
d.o.f=3
H0 : No serial correlation

Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
                         statistic p-value
Lag[1]                     0.01507  0.9023
Lag[2*(p+q)+(p+q)-1][8]    3.28506  0.6332
Lag[4*(p+q)+(p+q)-1][14]   4.72452  0.8028
d.o.f=3

Weighted ARCH LM Tests
------------------------------------
            Statistic Shape Scale P-Value
ARCH Lag[4]    0.2978 0.500 2.000  0.5853
ARCH Lag[6]    4.7944 1.461 1.711  0.1259
ARCH Lag[8]    5.0893 2.368 1.583  0.2395

Nyblom stability test
------------------------------------
Joint Statistic:  4.1596
Individual Statistics:              
mu     0.16397
ar1    0.07774
ma1    0.06603
ma2    0.05386
omega  0.57411
alpha1 1.27031
alpha2 1.05386
beta1  0.56587
gamma1 0.73976
gamma2 0.33343
shape  0.15746

Asymptotic Critical Values (10% 5% 1%)
Joint Statistic:         2.49 2.75 3.27
Individual Statistic:    0.35 0.47 0.75

Sign Bias Test
------------------------------------
                   t-value   prob sig
Sign Bias           0.9524 0.3410    
Negative Sign Bias  1.4660 0.1428    
Positive Sign Bias  0.6865 0.4925    
Joint Effect        3.3397 0.3422    


Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
  group statistic p-value(g-1)
1    20     24.02       0.1955
2    30     33.45       0.2599
3    40     45.94       0.2067
4    50     51.08       0.3919


Elapsed time : 0.820385 

Answer 1

我得到了老师的回答，他说gamma2和gamma1相比非常小，gamma2也非常接近于零。所以我们可以忽略这个价值。