# Weighted Mean - Decreasing Strength of Interactions

Decreasing Strength of Interactions

Consider the time series of an independent variable and a dependent variable, with observations sampled at discrete times . In many common situations, the value of at time depends not only on 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 for a window size .

$z_k=sum_{i=1}^m w_i_x_{k+1-i}.$
Range weighted mean interpretation
Range (1–5) Weighted mean equivalence
3.34–5.00 Strong
1.67–3.33 Satisfactory
0.00–1.66 Weak

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