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After reviewing the Wikipedia page on moving averages, the difference between the simple moving average and cumulative moving average are clear:

1) Simple moving average only considers the last n observations, and for every additional observation added to the average, the oldest one gets dropped

2) Cumulative moving average considers all prior observations

However, I am confused as to which moving average to use to smooth out data and identify trends.

As seen in the linked picture above, the cumulative moving average is quite distinctly different from both the observations themselves and the 4 period moving average. Is there a rule of thumb of when to use one or the other?

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    $\begingroup$ A cumulative moving average is a really bad idea for 'smoothing out data and analyzing trends' as you have pretty much seen for yourself here. A simple moving window is for this purpose, and good for a lot of applications, but has some notable disadvantages. Exponentially weighted moving averages tend to work better and not much more difficult to implement. More general exponential smoothing is the natural next step, but a little more complicated. See e.g. itl.nist.gov/div898/handbook/pmc/section4/pmc43.htm What's the right balance depends on the problem at hand. $\endgroup$
    – spaceisdarkgreen
    Commented Mar 17, 2018 at 3:08
  • $\begingroup$ Thanks for the link, that provided a good explanation of exponentially weighted moving averages. I feel given the context of my problem the simple moving average will work better for this case, but now I have a new tool to add to my arsenal. Cheers mate! $\endgroup$
    – user541285
    Commented Mar 18, 2018 at 22:43

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