In case of regression analyiss, we test the significance of model fit by using F-test. just like that, how to test the validity of the GARCH model?
usually, econometric softwares do not report F-statistic for GARCH model.
thanks in advance.
In order to test for the validity of your analysis when using GARCH models, you should make sure that the model adequately captures the dynamics of the data. In other words, make sure that standardised residuals and squared standardised residuals are free from serial autocorrelation (you can employ the Box-Pierce portmanteau statistic).
In addition, you have to make sure that your model capture all ARCH effects (employ Lagrange multiplier test)
dear proft. Amira Akl Ahmed thank you for your valuable reply
you have not mentioned about normality and homoscedasticity of the residuals. are they not required?. if they are required, how to test them.
can you please suggest any standard text for reference in this regard
The following three aspects of the residuals from fitted GARCH model should be tested:
1. The standardized residuals from the GARCH model should approach normal distribution. One can use Shapiro-Wilk test and Jarque-Bera normality test. Histogram of the residuals is also a good visual tool to check normality.
2. The standardized squared residuals from the GARCH model should not be autocorrelated. One can use Ljung-box Q-statistic for this purpose.
3. ARCH LM test on the residuals can also be conducted to check for remaining ARCH effects in the residuals.
thank you Najibullah Hassanzoy
your explanation is very much helpful to me.
once again thank you .
Najibullah Hassanzoy
"The standardized residuals from the GARCH model should approach normal distribution. One can use Shapiro-Wilk test and Jarque-Bera normality test. Histogram of the residuals is also a good visual tool to check normality"
This is right only if conditional normality of residuals is assumed. However, a researcher may use other distribution (e.g. student t, GED, skewed t, and skewed GED).
Dear Sister Ahmed,
That is true.
If the number of observations used is large enough, t-distribution may also approach normal distribution. Thus, the residuals from a GARCH model with t-distribution may also follow normal distribution.
However, the distribution of many economic series is flat-tailed, which require a GARCH with t-distribution. One should check the distribution of the variable before choosing the type of distribution to be used with GARCH estimation.
Thanks
thanks to all the professors who spent their valuable time in responding to my question.
how to examine the distribution of the variable before choosing the type of distribution to be used with GARCH estimation.(like student t, GED, skewed t, and skewed GED).
please respond to it
Srikanth Potharla
I highly recommend to use the book written by Chris Brooks. Its title is "Introductory Econometrics for Finance".
Srikanth Potharla
The distribution of the variable in question can be examined using the measures of skewness, kurtosis and Jarque-Bera.
To test the validity of GARCH model, after the estimation of volatility we need to check whether the model has adequatley captured the voltility of data or not, we need to run Residual Diagnostic test to check whether the data series is free from Serial correlation and ARCH effect or not (This includes 3 tests).
1. Correlogram - Q Statistics (Standardized Residuals)
2. Correlogram - Squared Standardized Residuals and
3. ARCH test
To test the validity of GARCH model, after the estimation of volatility we need to check whether the model has adequatley captured the voltility of data or not, we need to run Residual Diagnostic test to check whether the data series is free from Serial correlation and ARCH effect or not (This includes 3 tests).
1. Correlogram - Q Statistics (Standardized Residuals)
2. Correlogram - Squared Standardized Residuals and
3. ARCH test
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