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Date: 6-1-2016
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Date: 23-9-2021
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Date: 9-11-2021
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Given a sequence , an
-moving average is a new sequence
defined from the
by taking the arithmetic mean of subsequences of
terms,
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(1) |
So the sequences giving
-moving averages are
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(2) |
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(3) |
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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