Standardization of the residuals

A pre-requisite to much of the analysis is that the residual time series be standardized. The standardizing $z$ transform, $z = \frac{x - \mu}{\sigma}$, is applied to each time series

$$z = \frac{x - \bar x}{s},$$ (27)

where the computational formula for $s$ is

$$s = \sqrt {\frac{\sum x^2 - \frac{({\sum x})^2}{N}}{N-1}}.$$ (28)