# Does the wild bootstrap use residuals or standardised residuals

I have seen a few sources that describe the wild bootstrap as so:

For each bootstrap instance, compute a new $$y$$ based on:

$$y^*_i = \hat{y}_i+\hat{\epsilon}_iv_i$$

Where $$y^*_i$$ is the $$i^{th}$$ bootstrap instance, $$\hat{y}_i$$ is the original data, $$\hat{\epsilon}_i$$ is the residual and $$v_i$$ is a bootstrap variable with mean zero variance one.

One example would be the wikipedia page on bootstrapping for example here.

However, I've seen other sources saying that the wild bootstrap instead uses the standardised residuals like so:

For each bootstrap instance, compute a new $$y$$ based on:

$$y^*_i = \hat{y}_i+\frac{\hat{\epsilon}_i}{\sigma}v_i$$

Where $$y^*_i$$ is the $$i^{th}$$ bootstrap instance, $$\hat{y}_i$$ is the original data, $$\hat{\epsilon}_i$$ is the residual, $$v_i$$ is a bootstrap variable with mean zero variance one and $$\sigma$$ is the estimated standard deviation of the $$y_i$$ variables.

An example of this would be the Wu 1986 paper here.

Which of these is correct? I don't understand the logic behind using the standardised residuals here.