I have got the following output from a gjrGARCH model, and I need help to interpret it in order to decide whether it is already a good model and proceed with the forecast.
* GARCH Model Fit *
Conditional Variance Dynamics
-----------------------------------
GARCH Model : gjrGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : sstd
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
omega 0.000503 0.000324 1.5553 0.119881
alpha1 0.023633 0.003162 7.4744 0.000000
beta1 0.970088 0.000974 996.3224 0.000000
gamma1 0.010581 0.005669 1.8664 0.061986
skew 0.993806 0.018396 54.0224 0.000000
shape 9.056867 1.108510 8.1703 0.000000
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
omega 0.000503 0.000343 1.4653 0.142836
alpha1 0.023633 0.002997 7.8868 0.000000
beta1 0.970088 0.000214 4524.1078 0.000000
gamma1 0.010581 0.005480 1.9310 0.053485
skew 0.993806 0.017524 56.7121 0.000000
shape 9.056867 1.058729 8.5545 0.000000
LogLikelihood : -4150.073
Information Criteria
------------------------------------
Akaike 1.6473
Bayes 1.6550
Shibata 1.6473
Hannan-Quinn 1.6500
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.6489 0.4205
Lag[2*(p+q)+(p+q)-1][2] 1.5551 0.3485
Lag[4*(p+q)+(p+q)-1][5] 3.7025 0.2936
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 8.749 0.003097
Lag[2*(p+q)+(p+q)-1][5] 11.687 0.003364
Lag[4*(p+q)+(p+q)-1][9] 13.244 0.009368
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.1708 0.500 2.000 0.6794
ARCH Lag[5] 0.7991 1.440 1.667 0.7933
ARCH Lag[7] 1.7052 2.315 1.543 0.7794
Nyblom stability test
------------------------------------
Joint Statistic: 1.2345
Individual Statistics:
omega 0.57916
alpha1 0.42675
beta1 0.45756
gamma1 0.33651
skew 0.08674
shape 0.37510
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.49 1.68 2.12
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
t-value prob sig
Sign Bias 0.1196 0.9047955
Negative Sign Bias 2.0285 0.0425644 **
Positive Sign Bias 3.5114 0.0004496 ***
Joint Effect 17.7533 0.0004945 ***
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 17.08 0.58474
2 30 35.69 0.18282
3 40 51.63 0.08483
4 50 51.38 0.38050
I have a bunch of questions about it:
- if I look at Optimal Parameters and Robust Standard Errors I see that omega and gamma1 have p>0.05 which make them not statistically significant. How to make them significant? or can I neglect this result?
- Information Criteria: i know that this is important if the goal is forecasting. That is my goal but is 1.6473 a good number or it is too high?
- Weighted Ljung-Box Test on Standardized Residuals: I see the p>0.05 which make me accept the null hyp and that is good, however, the squared residuals have all p<0.05 which means that the squared residual ar correlated. How can I avoid that to have white noise also in the squared residuals?
- Adjusted Pearson Goodness-of-Fit Test, Weighted ARCH LM Tests, Nyblom stability test Sign Bias Test are kind of obscure to me and I do not know how to interpret them.
I would really appreciate any clear explanation which seems really hard to have looking on the web. Thanks
