Univariate context:

In this model the variance of the Gaussian distribution p_t^(k) is given by the recursive formula:  

$${\sigma_t^{_{(k)}}}^2 = 0.94{\sigma_{t-1}^{_{(k)}}}^2 + 0.06... ...^2,\quad \sigma_{-249}^{_{(k)}} = \vert x_{-249}^{_{(k)}}\vert.$$ (14)

The value of $\sigma_t^{_{(k)}}$ is not sensitive to the seed value $\sigma_{-249}^{_{(k)}}$ once the recursion has been applied 250 times or more. Of course, for the latter to be true, the seed value must be a reasonable value like the one used in expression . The repeated application of the recursive expression  will allow the specification of 1000 prediction-realization pairs starting with (p_1^(k),x_2^(k)) and ending with (p_1000^(k),x_1001^(k)). These pairs are the starting point of the univariate performance analysis of the model.