Talk:Moving average/Archives/2014

This is an archive of past discussions about Moving average. Do not edit the contents of this page. If you wish to start a new discussion or revive an old one, please do so on the current talk page.

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)

Some large updates

I am starting a possibly large edit to this page, so wanted to document some of my thinking here:

1. I agreed with comment about Introduction needing some work. I tried to add an intro and generalize it.

2. There seem to be 3 terms being used: moving average, rolling average, running average. Although there is a separate section for running average, I think this has the same meaning as the other two. This may be controversial, so here are some links showing that the term running average is used to describe a moving average, not necessarily a cummulative moving average:

Wolfram Mathworld redirects running average to moving average.

Columbia University Climate data library

another redirection from running average

Used on Intel documents

Linux developers using the term

The above is not meant to be authoritative, but merely to show that the term "running average" is also commonly used to mean moving average. I am sure there are as many examples where running average means cummulative average. But for this reason, I think a more appropriate term is "cummulative moving average" so I have gone with that.

There are several more changes I want to make, but out of time. Will track them here for discussion. (Econotechie (talk) 19:03, 19 September 2008 (UTC))

Discontiguous exponential averaging

Does the concept of discontiguous exponential averaging (DEA) also belong in this article? The earliest reference I can find is

John C. Gunther, "Algorithm Alley: Discontiguous Exponential Averaging", Dr. Dobb's Journal, Sept. 1998, ISSN 1044-789X, vol 23 no 9, pp. 117-119, 125. (print version)

John C. Gunther, Discontiguous Exponential Averaging, Sept. 1, 1998, http://www.ddj.com/architect/184410671 (online version)

This is another take on decaying averages, and is better suited to sampling statistics where there is not a fixed interval between samples (such as "daily"). It seems to see widest use in software applications, rather than accounting, etc. -- Dmeranda (talk) 19:20, 6 October 2008 (UTC)

Graphs

Hi there - I think this article is screaming for some graphic examples. It would be nice to have one time series and show the different types of average on it, perhaps with different parameters. If someone has access to standard statistical packages it should not be too hard. Thanks. 205.228.104.142 (talk) 03:40, 30 September 2009 (UTC)

Agree. Animated graphs would be even awesomer. 129.10.245.158 (talk) 22:56, 13 December 2010 (UTC)

Slutzky-Yule effect

I see no mention of the Slutzky-Yule effect. Paradoctor (talk) 10:36, 14 November 2009 (UTC)

Spencer's average

Hi, I was investigating Spencer's formula, and it looks that it look almost like 74.0*lanczos_2(x/4.3), which is low pass filter (Lanczos filter is windowed&smoothed version of sinc filter, which is ideal low-pass filter), but coefficients have small errors still differing from lanczos (something like 1-3%). I cannot find any good and available sources of origin of this coefficients (but i assume they are older than Lanczos filter). Just look at this http://i.imgur.com/rkf2M.png Is this is coincidence, or they are releated? --83.18.219.251 (talk) 05:47, 2 January 2011 (UTC)

Exponential moving average

Using the original formula in the article

$S_{t}=\alpha \times Y_{t}+(1-\alpha )\times S_{t-1}$

you can never arrive at this formulation

$S_{t}=\alpha \times (Y_{t-1}+(1-\alpha )\times Y_{t-2}+(1-\alpha )^{2}\times Y_{t-3}+...+(1-\alpha )^{k}\times Y_{t-(k+1)})+(1-\alpha )^{k+1}\times S_{t-(k+1)}$

Because the first term in there is

$\alpha \times Y_{t-1}$

not

$\alpha \times Y_{t}$

You need

$S_{t}=\alpha \times Y_{t-1}+(1-\alpha )\times S_{t-1}$

to get the first term right and the rest of the formula.

I check with reference [4] in the article and it's the above formula I gave here. — Preceding unsigned comment added by 222.248.5.95 (talk) 12:25, 21 March 2012 (UTC)

That means the second long formula you wrote above is incorrect. The first formula is correct. You need the current value of Y, not the prior value, to get the current value of S.

The problem with reference 4 is that it uses a nonstandard approach to calculating the moving average. The confusion seems to have made its way into the article. ~Amatulić (talk) 14:48, 21 March 2012 (UTC)

The second formula above is in the original article. I did not come up with that formula. Using

$S_{t}=\alpha \times Y_{t}+(1-\alpha )\times S_{t-1}$

one should get something like this

$S_{t}=\alpha \times (Y_{t}+(1-\alpha )\times Y_{t-1}+(1-\alpha )^{2}\times Y_{t-2}+\cdots +(1-\alpha )^{k}\times Y_{t-k})+(1-\alpha )^{k+1}\times S_{t-(k+1)}$

I think this is what I got. — Preceding unsigned comment added by 222.248.5.95 (talk) 04:37, 22 March 2012 (UTC)

I used a poor choice of words above. The formulas are correct depending on which reference you use. The article uses sources that define the exponential moving average in different ways, one using the previous Y value to get the current average, and one using the current Y value to get the current average. The article should settle on one standard and stick with it, possibly mentioning alternative methods. I would advocate using the current value of Y to calculate the current value of the moving average, because that is by far the dominant usage in the financial world, and in digital signal processing, and it is also the best digital representation of an analog lowpass RC filter. ~Amatulić (talk) 17:12, 22 March 2012 (UTC)

You were right regarding the time, whether it's current or previous, it should have been consolidated to one time base to save the confusion. Agree most of us would use current data to estimate the current average or current parameter, I am in for this approach too because it seemed so straight forward and logical. Just like the Kalman filter I used to know. — Preceding unsigned comment added by 222.248.5.95 (talk) 04:39, 23 March 2012 (UTC)

The article appears to be lacking a citation for the equation $\alpha =2/(N+1)$ . 212.183.128.119 (talk) 12:38, 11 June 2012 (UTC)

Comment on external links

I added a link to my blog MovingAverages.php Café math : Moving Averages as I think it complements well the present article by introducing the method of generating series and the technique of z-tranform. — Preceding unsigned comment added by 89.158.142.199 (talk) 16:33, 8 April 2012 (UTC)

Captions needed on images

The first two images in the article are presented with no captions describing what is being displayed. Could whoever added those images provide a caption, at least a small one? Regards. Gaba ^(talk) 19:00, 25 September 2013 (UTC)

redundant "Exponential moving average"

Two articles present similar content:

Sorry, I do not have enougth motivation/time to check further and to manage the potential merge.

Oliver H (talk) 09:06, 6 March 2014 (UTC)

Add section for triple moving average

The triple moving average to remove inversion defects is described in the SMA section. Perhaps it should be given a section of its own, with reasoning why it works. One source that explains the workings (technical) is http://judithcurry.com/2013/11/22/data-corruption-by-running-mean-smoothers/ . This page does say that the window proportions between iterations is 1.3371, which is incorrect given the equation solved to obtain the number, which should be 1.4303. However, the explanation of where the ratio comes from is helpful.

Rjmartinator (talk) 22:20, 21 May 2014 (UTC)