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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.

enter image description here

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?

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