Univariate context:

In this model, as in all subsequent models described below, the conditional distribution p_t^(k) is predefined to be a Gaussian distribution with variance ${\sigma_t^{_{(k)}}}^2$. The difference between this and subsequent models lies only in the manner $\sigma_t^{_{(k)}}$ is generated from the price change history of a given series. For this model:

$${\sigma_t^{_{(k)}}}^2 = {1\over250}\sum_{i=0}^{249}{x_{t-i}^{_{(k)}}}^2$$ (11)

and this along with x_t^(k) constitutes the full specification of the prediction-realization pairs that form the starting point of the univariate performance analysis of the model.