Moving Average
المؤلف:
Kenney, J. F. and Keeping, E. S.
المصدر:
"Moving Averages." §14.2 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand
الجزء والصفحة:
...
3-5-2021
3069
Moving Average
Given a sequence ![<span style=]()
{a_i}_(i=1)^N" src="https://mathworld.wolfram.com/images/equations/MovingAverage/Inline1.gif" style="height:19px; width:38px" />, an 
-moving average is a new sequence ![<span style=]()
{s_i}_(i=1)^(N-n+1)" src="https://mathworld.wolfram.com/images/equations/MovingAverage/Inline3.gif" style="height:19px; width:51px" /> defined from the 
by taking the arithmetic mean of subsequences of 
terms,
 |
(1)
|
So the sequences 
giving 
-moving averages are
and so on. The plot above shows the 2- (red), 4- (yellow), 6- (green), and 8- (blue) moving averages for a set of 100 data points.
Moving averages are implemented in the Wolfram Language as MovingAverage[data, n].
REFERENCES:
Kenney, J. F. and Keeping, E. S. "Moving Averages." §14.2 in Mathematics of Statistics, Pt. 1, 3rd ed. Princeton, NJ: Van Nostrand, pp. 221-223, 1962.
Whittaker, E. T. and Robinson, G. "Graduation, or the Smoothing of Data." Ch. 11 in The Calculus of Observations: A Treatise on Numerical Mathematics, 4th ed. New York: Dover, pp. 285-316, 1967.
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