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The fitted standardized innovations from a GARCH model will have (approximately) zero mean and unit variance regardless of the scaling of the original data. This is by construction of the GARCH model which assumes that standardized innovations have (exactly) zero mean and unit variance.

In a simple GARCH(1,1) model, the constant $\omega$ in the conditional variance equation $$ \sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2 $$ takes care of that. Scale your original data by $c$, and the (estimate of) $\omega$ will scale by $c^2$, ensuring that the (fitted) standardized innovations have unit variance.

The fitted standardized innovations from a GARCH model will have (approximately) zero mean and unit variance regardless of the scaling of the original data. This is by construction of the GARCH model which assumes that standardized innovations have (exactly) zero mean and unit variance.

In a simple GARCH(1,1) model, the constant $\omega$ in the conditional variance equation $$ \sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2 $$ takes care of that. Scale your original data by $c$, and the (estimate of) $\omega$ will scale by $c^2$, ensuring that the (fitted) standardized innovations have (approximately) unit variance.

The fitted standardized innovations from a GARCH model will have (approximately) zero mean and unit variance regardless of the scaling of the original data. This is by construction of the GARCH model which assumes that standardized innovations have (exactly) zero mean and unit variance.

In a simple GARCH(1,1) model, the constant $\omega$ in the conditional variance equation $$ \sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2 $$ takes care of that. Scale your original data by $c$, and the (estimate of) $\omega$ will also scale by $c$, ensuring that the (fitted) standardized innovations have unit variance.

The fitted standardized innovations from a GARCH model will have (approximately) zero mean and unit variance regardless of the scaling of the original data. This is by construction of the GARCH model which assumes that standardized innovations have (exactly) zero mean and unit variance.

In a simple GARCH(1,1) model, the constant $\omega$ in the conditional variance equation $$ \sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2 $$ takes care of that. Scale your original data by $c$, and the (estimate of) $\omega$ will scale by $c^2$, ensuring that the (fitted) standardized innovations have unit variance.

The fitted standardized innovation from a GARCH model will have (approximately) zero mean and unit variance regardless of the scaling of the original data.

The fitted standardized innovations from a GARCH model will have (approximately) zero mean and unit variance regardless of the scaling of the original data. This is by construction of the GARCH model which assumes that standardized innovations have (exactly) zero mean and unit variance.

In a simple GARCH(1,1) model, the constant $\omega$ in the conditional variance equation $$ \sigma_t^2=\omega+\alpha_1\varepsilon_{t-1}^2+\beta_1\sigma_{t-1}^2 $$ takes care of that. Scale your original data by $c$, and the (estimate of) $\omega$ will also scale by $c$, ensuring that the (fitted) standardized innovations have unit variance.