moving average

A moving average is a sequence of arithmetic meansMathworldPlanetmath taken over a fixed interval moved along consecutive data points from an infinite (or sufficiently large) set of data points. That is, given a sequence ax,,ax+k and an interval n, the average


is taken for each value (x+n)<i<(x+k-n).

Plotting a moving average can help to smooth out an extremely jagged curve so as to allow one to see larger patterns. For example, take this plot of the number of (nondistinct) prime factorsMathworldPlanetmath function ( Ω(n) for 20<n<120:

If instead we plot a moving average with an interval of 40, we get a smoother curve:

Though in all honesty, moving averages are not all that useful in number theoryMathworldPlanetmath. They are much used, however, in statistics and fields using statistics, such as physics and economics. In economics, for example, a moving average over an interval of say, 3 months, helps investors worry less about the wild hectic fluctuations in a day of trading and focus on the overall direction of a given stock. In physics, to give another example, a yearly moving average of parts per million of carbon dioxide in the atmosphere of the Earth smooths out the yearly dips of summer to show that overall carbon dioxide is going up, contributing to significant global warming.

Title moving average
Canonical name MovingAverage
Date of creation 2013-03-22 16:45:03
Last modified on 2013-03-22 16:45:03
Owner PrimeFan (13766)
Last modified by PrimeFan (13766)
Numerical id 9
Author PrimeFan (13766)
Entry type Definition
Classification msc 62M10
Classification msc 26D15
Classification msc 11-00
Classification msc 91B84