Using Sign Bias Tests to Assess GARCH Asymmetry

Summary

The document asks how residuals should be constructed for the sign bias test, which regresses squared residuals on an indicator for whether the preceding residual was negative. It distinguishes two possible uses: checking for asymmetric effects in returns and evaluating whether a symmetric GARCH model captures volatility adequately. The question cites the residual definition as the return minus its conditional mean, while noting that some explanations use residuals from a fitted symmetric GARCH model.

The document does not provide a resolution, derivation, empirical example, or guidance on how to choose between these residual definitions. It is therefore useful chiefly for identifying that the test’s interpretation depends on how residuals are obtained and on the model being assessed. Readers should consult the original methodological source or a fuller treatment before applying the test; the document itself is a question rather than an answer.

Key ideas

• The sign bias test checks whether negative past residuals help explain current squared residuals.
• The test regresses squared residuals on an indicator for a negative preceding residual.
• The question distinguishes testing for asymmetry from assessing a symmetric GARCH model’s adequacy.
• The document raises, but does not resolve, which residuals to use for each purpose.

Tags

# The difference in sign bias test in detecting the exist of asymmetric effects and the adequacy of symmetric GARCH model.


# The difference in sign bias test in detecting the exist of asymmetric effects and the adequacy of symmetric GARCH model.












The question is that I want to know whether there is difference in the applying of sign bias test in detecting the exist of asymmetric effects and the adequacy of symmetric GARCH model.

In the definition of sign bias test, we need to do the t test for the coefficient $\beta$ in the regression equation $\hat{\epsilon}_t^2 = \alpha + \beta S_{t-1}^- + z_t$, where $\hat{\epsilon}_t$ is the estimated residual, $S_{t-1}^-$ is the dummy function that $\hat{\epsilon}_{t-1} < 0 $ and 0 otherwise and $z_t$ is the noise.

My quiz is that how do I get the estimated $\hat{\epsilon}$. In the original paper by Engle and Ng http://www.finance.martinsewell.com/stylized-facts/volatility/EngleNg1993.pdf

It explained that $\hat{\epsilon}_t$ is from the equation that $\hat{\epsilon}_t = y_t - \mu_t$. My understanding is that, if $\hat{\epsilon}_t$ is from the that equation, then it is only with the purpose to check the exist of asymmetric effects. But some material explain $\hat{\epsilon}_t$ is estimated from a symmetric GARCH model, for example, GARCH(1,1), if we want to show whether a symmetric GARCH model is adequate in describing the asymmetric effects. I am confused about it.

Thanks in advance.

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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.