Editing Weighted arithmetic mean (section)

===Decreasing strength of interactions===

Consider the time series of an independent variable <math>x</math> and a dependent variable <math>y</math>, with <math>n</math> observations sampled at discrete times <math>t_i</math>. In many common situations, the value of <math>y</math> at time <math>t_i</math> depends not only on <math>x_i</math> but also on its past values. Commonly, the strength of this dependence decreases as the separation of observations in time increases. To model this situation, one may replace the independent variable by its sliding mean <math>z</math> for a window size <math>m</math>.

:<math>z_k=\sum_{i=1}^m w_i x_{k+1-i}.</math>