GARCH or TARCH model when assymetric volatility but GARCH(1,1) already performs well? I have the following question: I am analyzing Brent Oil returns and I have found that there's a significant negative sign bias. So first, I have tried with a GARCH(1,1) and it turns out that completly cleans the ACF, so there are no significant autocorrelations left, and adjusts quite decently to the data.
However, due to the presence of negative sign bias I've decided to perform a TARCH(1,1) but it turns out that performs dramatically worse than GARCH(1,1), as ACF is not cleant and residuals still have lot of noise. 
Any suggestion of how I should tackle this issue?
Thank you very much!
 A: Citing the vignette of "rugarch" package in R,

The sign bias test of Engle and Ng (1993) <...> tests the presence of
  leverage effects in the standardized residuals (to capture possible
  misspecification of the GARCH model), by regressing the squared
  standardized residuals on lagged negative and positive shocks as
  follows:
$$ \hat z_t^2 = c_0 + c_1 I\{\hat\varepsilon_{t-1}<0\} + c_2
> I\{\hat\varepsilon_{t-1}<0\} \cdot \varepsilon_{t-1} + c_3
> I\{\hat\varepsilon_{t-1}\geqslant 0\} \cdot \varepsilon_{t-1} + u_t $$
where $\hat\varepsilon_t$ are the estimated residuals from the GARCH
  process. The Null Hypotheses are $H_0: \ c_i = 0$ (for
  $i = 1, 2, 3$), and that jointly $H_0: \ c_1 = c_2 = c_3 = 0$. <...> [If
  rejected,] using instead a model such as the apARCH would likely
  alleviate these effects.

If one, several or all the hypotheses are rejected, the idea is to use a model that allows for asymmetric effects such as GJR-GARCH, APARCH, TARCH. (Hence, you may try the ones you have not tried yet.)
However, if you are unable to obtain a satisfactory model that allows for asymmetry, perhaps using a relatively good model without assymetry will be a lesser evil than using a poor asymmetric model. The model choice is essentially an empirical question. You could try doing out-of-sample performance evaluation to select the model that suits your needs best.
References


*

*Engle, Robert F., and Victor K. Ng. "Measuring and testing the impact of news on volatility." The Journal of Finance 48.5 (1993): 1749-1778.

*Ghalanos, Alexios. "Introduction to the rugarch package." Version 1.3-1 (2015).

