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

Read more about this topic:  Weighted Mean

Famous quotes containing the words interactions, decreasing and/or strength:

    The exercise of power is determined by thousands of interactions between the world of the powerful and that of the powerless, all the more so because these worlds are never divided by a sharp line: everyone has a small part of himself in both.
    Václav Havel (b. 1936)

    As men get on in life, they acquire a love for sincerity, and somewhat less solicitude to be lulled or amused. In the progress of the character, there is an increasing faith in the moral sentiment, and a decreasing faith in propositions.
    Ralph Waldo Emerson (1803–1882)

    Why, therefore, should we do ourselves this wrong,
    Or others—that we are not always strong—
    That we are sometimes overborne with care—
    That we should ever weak or heartless be,
    Anxious or troubled—when with us is prayer,
    And joy and strength and courage are with Thee?
    Richard Chenevix Trench (1807–1886)