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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   

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GARCH Model : gjrGARCH(1,1)

Mean Model  : ARFIMA(0,0,0)

Distribution    : sstd 


Optimal Parameters

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        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

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Akaike       1.6473

Bayes        1.6550

Shibata      1.6473

Hannan-Quinn 1.6500


Weighted Ljung-Box Test on Standardized Residuals

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                        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

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            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

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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

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                   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:

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  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

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