Talk:Moving average

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This article may be too technical for a general audience. Please help improve this article by providing more context and better explanations of technical details to make it more accessible, without removing technical details.

The introduction to the article seems to assume that the reader already knows the material that the article imparts. The body of the article is comprehensible, but not easily. 64.26.98.90 20:41, 8 November 2007 (UTC)

Perhaps this is technical but it is about the only place I was able to find enough detail to actually code and verify my EMA. I appreciate the author(s) very much! Well done! Brittlowry (talk) 22:52, 1 January 2008 (UTC)

[edit] Merge with Temporal mean

It is proposed to merge Temporal mean into this article.  --Lambiam 22:29, 3 May 2008 (UTC)

I note that recently the temporal mean article was modified to imply that the term is a synonym of 'moving average'. I am not really familiar with the term 'temporal mean', but some research seems to indicate that this is often not what 'temporal mean' means. (So far, I have not encountered any usages where it is clear that a moving average is meant, so I don't know whether 'temporal mean' is ever synonymous with moving average.)

For instance, this page in a vibration testing book defines temporal mean as a limit of an integral as the bound of the integral goes to infinity. Not too much like a moving average. This oceanography article seems to define it as the ratio of two infinitely bounded integrals. This page in an environmental text defines it as a mean of a fluctuating quantity over a time period, and states it is constant if the time is sufficiently long. It then gives an example which is an integral over a time period divided by the duration. It does not seem to be like a continuous-function extension of a moving average because the starting point of the period is fixed (at 0), and does not move like the period of a moving average would.

Thus to me it looks like there needs to be a separate article, since (in at least some usages) there are pretty distinct differences between 'moving average' and 'temporal mean'. -R. S. Shaw (talk) 03:00, 5 May 2008 (UTC)

Since the meaning described in the Temporal mean article (also before my recent modifications) does not cover most of these examples, and it is not likely that anytime soon someone is going to write an article collecting and describing all disparate meanings that have been used – none of which appear to have appreciable currency – it is then perhaps indeed better that that article is deleted as having no encyclopedic value and being potentially misleading.  --Lambiam 20:47, 5 May 2008 (UTC)

I don't see why you think a temporal mean article would have no encyclopedic value. The fact that there are various references to it which will pop up in a google search, and that many of the usages assume knowledge of what the term means, seems to me to show that it needs explanation in a place like Wikipedia. It's clearly not a hugely popular term (not like moving average, which is used widely), but that does not imply it should not be covered. Since the size of Wikipedia does not have to be limited by printing costs but only by the reasonableness of covering the subject. That this term shows up in multiple technical fields suggests to me that it is worthy of coverage. Two of the three references I gave above seem fairly consistent about the meaning, and the other might be a compatible extension of the same concept, so it's not clear to me that that there are lots of disparate meanings to be collected. Even if there are, that's not a reason not to have an article: Wikipedia articles can start out as stubs and grow over years to provide better coverage.

The only area I suspect has the potential for being misleading is whether in fact the term is used with discrete sets of values (versus continuous functions), which the article starts out covering. All the usages I looked at in my recent search had to do with integrals of continuous functions. Do you have knowledge that the term is used with non-continuous data sets? Where did you pick up the idea that temporal mean was the same or similar to a moving average? -R. S. Shaw (talk) 04:22, 6 May 2008 (UTC)

The first two of your references have totally different meanings. If the process or signal whose temporal mean is taken is a mapping T → R in which T is a time domain and R is the range of possible outcomes, then the first defines the temporal mean as belonging to R and the second as belonging to T. The first one fails to consider the possibility that the limit does not exist; it states without blinking: "These fluctuations disappear as T increases indefinitely", which is of course in general not true at all; take e.g. the signal f(t) = sin(log(t+1)), whose time average keeps moving around with the same amplitude. The third one is strange. It states: "If the time period is sufficiently long, the temporal mean values are constant over time." For the definition given, that is a meaningless statement, as the temporal mean is not defined as a function of time. It would make sense if the moving time average is meant. This seems to be confirmed by the text on p. 100, where the change of the temporal mean is considered. Altogether three different definitions, of which only the middle one is clear.

The present article Temporal mean has no encyclopedic value. Moreover, it is misleading if readers who encounter the term somewhere look it up and find (very likely, as you have shown) a different meaning here than the intended one. I see no reasonable way of fixing the article so that it is verifiable and gives the reader a reasonable chance of finding the appropriate meaning represented. Yes, if someone replaces that article with a well-written and well-sourced overview of various meanings of the term temporal mean, then I'll be all in favour of keeping that well-written and well-sourced encyclopedic overview. However, that is not going to happen any time soon. In the meantime we have an article that is such that readers are actually better off if they don't find it. So why should we keep it around then?

The moving average is an average over a time window. The purpose is usuallly to smooth a slow-moving process that is subject to somewhat random jitter so as to detect the drift. So it is an average over time, where you let the time window move. In most applications the data is sampled at regular intervals (sales in January, sales in February, ...), but is actually an aggregation of a much finer signal (sale between January 1, 00:00:00 and January 1, 00:00:01, ...). The aggregation is effectively an integral, and the sum of these integrals over the months of the window is the same as the integral over the whole window. It is just not presented like that to the kind of people who use this kind of stuff, such as sales managers.  --Lambiam 20:56, 6 May 2008 (UTC)

I understand what a moving average is, but is there any reason to believe it is the same as a temporal mean in any context? A moving average maps a dataset into another dataset (or a function of time into another function of time), but a temporal mean seems to map a dataset into a value (or a function involving a time parameter into a function not having a time parameter). -R. S. Shaw (talk) 18:57, 7 May 2008 (UTC)

Each value of the moving average is a temporal mean. If you look at the formula in this article given for SMA, the right-hand side of the definition is a temporal mean (for a finite time window).  --Lambiam 07:48, 8 May 2008 (UTC)