Dispersion is a derived series describing the distribution of the original values.

In statistics, variance is frequently used to measure the degree of dispersion of a set of data. We can also apply variance to calculate dispersion, which we’ll refer to as the ‘variance method’.

The dispersion series S for a time series X is calculated as:

s_i=sum((x_j-a)²)/(n-1),j∈[1,n]

Where n=l+1, which is the length of X[-(l+1)]_i+1; x_j is the j-th element of X[-(l+1)]_i+1; a is the average of the values in X[-(l+1)]_i+1.

SPL routine:

The dispersion series S is calculated in cell A3. The function var@s(…) computes the variance.

Calculation result example:

In the figure, the x-axis represents the sequence index, the left y-axis represents the values of the original series X, and the right y-axis represents the values of the dispersion S. In the legend, X is the original series and S is the dispersion. (Because the first five time points have no dispersion, the figure only displays the dispersion for the subsequent 95 time points).