# Standardized residual by GARCH model shows bimodal distribution, is it normal?

I fit a GARCH(1,1) model on the spread of 2 correlated assets :

the GARCH model shows this summary:

==========================================================================
coef    std err          t      P>|t|    95.0% Conf. Int.
--------------------------------------------------------------------------
omega          0.2066  5.839e-02      3.537  4.042e-04 [9.211e-02,  0.321]
alpha[1]       0.6416  5.479e-02     11.712  1.107e-31   [  0.534,  0.749]
beta[1]        0.3584  6.020e-02      5.953  2.640e-09   [  0.240,  0.476]
==========================================================================


From this point, nothing weird, but then when I plot the standardized residual by their conditional volatility :

In order to retrieve entry/exit signals for my strategy, I'm doing a 2-tails test on the distribution of these standardized residual. However, as you can see, the distribution is very weird :

Is it normal to have such bimodal distribution for a standardized residual by a GARCH model ? I'm asking because this is definitely not something I was expecting (standard normal distribution, or at least t-student with fatter tails), neither something I found on the Internet as what we can expect for a GARCH std residual.. What did I miss here ?

• @JeremLachkar, not sure if I understand your question. Suppose the cond. mean model is $x_t=\mu_t+\varepsilon_t$ where $\mu_t$ is a function of the past or of an exogenous variable that is available at time $t$. Then the cond. variance of $x_t$ is the (cond.) variance of $\varepsilon_t$. The unconditional variance of $x_t$ is something else, but you probably (?) do not need that as it probably does not make sense to ignore conditioning information that is readily available. Commented Apr 17, 2023 at 10:38