Evaluating an eGARCH Model with Residual and Stability Diagnostics
Summary
The document presents an eGARCH(1,1) fit to weekly Bitcoin log returns over a multi-year sample, using a generalized error distribution and a date-related dummy variable. The broader research aim is to compare volatility dynamics across Bitcoin, Ethereum, and the S&P 500. The reported output includes parameter estimates, robust standard errors, information criteria, Ljung–Box tests on standardized and squared residuals, ARCH tests, a Nyblom stability test, and a goodness-of-fit test. Most listed residual tests have p-values above conventional rejection thresholds, while estimated model parameters are mostly statistically significant.
The author asks how to decide whether the model is adequate for interpretation. The output alone does not establish that it is: the Nyblom joint statistic and one individual statistic are undefined, and the robust p-value for the variance dummy is not significant. Diagnostics that fail to reject residual dependence or distributional misfit are not proof of correct specification. The excerpt gives no competing-model comparison, out-of-sample forecast evaluation, or robustness analysis, so conclusions about model suitability and the event effect remain limited.
Key ideas
- The example fits an eGARCH(1,1) model with a generalized error distribution to weekly Bitcoin returns and includes a date dummy.
- Residual and squared-residual tests show no detected serial dependence at the reported lags, but this does not prove correct specification.
- The Nyblom stability output contains undefined statistics, limiting interpretation of parameter stability.
- The robust test for the variance dummy is not statistically significant in the displayed output.
- Model acceptance would require further comparison and validation, which the document does not report.
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Full text
# eGARCH(1,1) model evaluation (R). How to assess model integrity?
# eGARCH(1,1) model evaluation (R). How to assess model integrity?
I am using GARCH modelling for my bachelor thesis in Economics. I am entirely new to the concept, and have only been looking into these kind of models for about a week now. I am trying to do a comparison of volatility dynamics between Bitcoin, Ethereum, and the S&P 500. I was wondering if anybody could help me with the evaluation of output.
Right now I have settled on weekly log returns from Bitcoin of the last 6 years. I am using a eGARCH(1,1)-GED model, as I think that it suits my data the best. I have done a lot of iteration over different models/distributions. I also included a dummy variable for a specific date of a major global event to assess its effect on the data.
Given the p-values of 0 for the coefficients and the p-values of > 0.05 for the residuals tests' and the Goodness-of-Fit test, it looks good to me. Anyways, my question is - given my lack of experience - how do I further evaluate my model? When can I accept the model for further analysis and interpretation?
Thank you!
```
* GARCH Model Fit *
*---------------------------------*
Conditional Variance Dynamics
-----------------------------------
GARCH Model : eGARCH(1,1)
Mean Model : ARFIMA(0,0,0)
Distribution : ged
Optimal Parameters
------------------------------------
Estimate Std. Error t value Pr(>|t|)
mu 0.005174 0.000000 30818.655 0
mxreg1 -0.007587 0.000095 -79.822 0
omega -0.195159 0.000346 -563.742 0
alpha1 0.026858 0.000067 398.347 0
beta1 0.956950 0.000686 1394.664 0
gamma1 -0.171288 0.000485 -353.122 0
vxreg1 -0.047483 0.000306 -155.024 0
shape 1.060467 0.002674 396.640 0
Robust Standard Errors:
Estimate Std. Error t value Pr(>|t|)
mu 0.005174 0.000003 1940.4508 0.000000
mxreg1 -0.007587 0.000237 -32.0510 0.000000
omega -0.195159 0.027368 -7.1310 0.000000
alpha1 0.026858 0.000505 53.1471 0.000000
beta1 0.956950 0.097386 9.8264 0.000000
gamma1 -0.171288 0.036241 -4.7263 0.000002
vxreg1 -0.047483 0.030302 -1.5670 0.117122
shape 1.060467 0.209286 5.0671 0.000000
LogLikelihood : 342.6141
Information Criteria
------------------------------------
Akaike -2.1313
Bayes -2.0358
Shibata -2.1326
Hannan-Quinn -2.0931
Weighted Ljung-Box Test on Standardized Residuals
------------------------------------
statistic p-value
Lag[1] 0.8471 0.3574
Lag[2*(p+q)+(p+q)-1][2] 0.8474 0.5505
Lag[4*(p+q)+(p+q)-1][5] 2.0499 0.6067
d.o.f=0
H0 : No serial correlation
Weighted Ljung-Box Test on Standardized Squared Residuals
------------------------------------
statistic p-value
Lag[1] 0.1784 0.6727
Lag[2*(p+q)+(p+q)-1][5] 1.2104 0.8105
Lag[4*(p+q)+(p+q)-1][9] 2.9158 0.7728
d.o.f=2
Weighted ARCH LM Tests
------------------------------------
Statistic Shape Scale P-Value
ARCH Lag[3] 0.1003 0.500 2.000 0.7515
ARCH Lag[5] 1.2961 1.440 1.667 0.6475
ARCH Lag[7] 2.1301 2.315 1.543 0.6898
Nyblom stability test
------------------------------------
Joint Statistic: NaN
Individual Statistics:
mu 0.03159
mxreg1 0.03045
omega 0.03250
alpha1 0.03266
beta1 NaN
gamma1 0.03008
vxreg1 0.03402
shape 0.03272
Asymptotic Critical Values (10% 5% 1%)
Joint Statistic: 1.89 2.11 2.59
Individual Statistic: 0.35 0.47 0.75
Sign Bias Test
------------------------------------
Adjusted Pearson Goodness-of-Fit Test:
------------------------------------
group statistic p-value(g-1)
1 20 24.85 0.1654
2 30 34.92 0.2073
3 40 36.57 0.5811
4 50 54.15 0.2843
Elapsed time : 0.2744429
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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.