Lets say I have a GARCH(1,1) model,

First, I model the conditional MEAN,

$$Y_t=\delta+\beta Y_{t-1}+\varepsilon_t$$

NextI gather the residuals $\varepsilon_t$ and model the conditional variance,

$$h_t=\omega + \alpha_i\varepsilon_{t-1}^2+\beta_ih_{t-1}$$

I need to get the standard residuals,

my attempt at this is,


Is this correct?

I am struggling to find this in any textbooks or papers so a reference would be appreciated if possible!

  • $\begingroup$ Thanks Richard, yes! $\endgroup$ Commented Jun 10, 2019 at 12:06
  • $\begingroup$ Indeed, when we talk about standardization, we are talking about "uniforming" the standard deviations. $\sqrt{r_t}$ is as good of an approximation for it as we can get (unless the process actually follows an exact GARCH, which never happens) $\endgroup$
    – David
    Commented Jun 10, 2019 at 14:16

1 Answer 1


This is correct.


  • $\begingroup$ Thanks very much for your help! $\endgroup$ Commented Jun 10, 2019 at 12:07
  • 1
    $\begingroup$ @FrancisOrigi, You are welcome! $\endgroup$ Commented Jun 10, 2019 at 12:07

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