# How to detect GARCH parameters must be updated?

I use a standard GARCH formulation:

$$\hat{\sigma}^2_{t+1} = \omega + \alpha r^2_t + \beta\hat{\sigma}^2_t$$

with $r_t = \sigma_t \varepsilon_t$ in order to have a daily estimate of volatility of equities (Brazilian equities). I would like to understand how frequently the GARCH parameters need to be re-estimated or even if there exists a test to detect that the volatility regime has changed. I don't think that parameters need to be re-estimated for every new return, but how do I know that after N returns they aren't significant.

I am monitoring the long term volatility $V_L$ ($V_L = \frac{\omega}{1 - \alpha - \beta}$) by re-estimating the parameters every day and comparing that result with the first set of parameter. But its standard error is quite huge and I don't think it is a good indicator to follow.

In blue we have the first long term volatility, in black the daily estimate and red is the rolling standard deviation. All using a 3 years moving window.

So can anyone suggest any measure which helps me detect how long the GARCH parameters have to be updated?