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Moving average and moving-average model are two quite different animals, but they seem to be conflated in the name and the description of the tag. The excerpt implies moving average, while the full Wiki considers moving-average model, although the description is not quite correct.

The confusion has been experienced in practice with users misinterpreting the real object of the question and posting answers that address the wrong object. Hence, the problem is real, not just theoretical.

What can we do? I suggest creating two separate tags, because these two objects are quite different but easily confused, especially when hidden under the same tag. Tag names would be, naturally, moving-average and moving-average-model. The Wiki excerpt of each tag would include a warning that there is another similar tag but with quite a different object under it.

Since one of the tags already exists, what remains to be done is to create the other tag and retag questions appropriately. There are 134 of them under the tag; one can go over all of them one by one.

Does that sound reasonable? Should we do something else? Or do nothing?

Edit: The differences between the two are the clearest in a forecasting context.

  • In moving average, $\hat x_{t}=\alpha_1 x_{t-1}+\dots+\alpha_q x_{t-q}$ where $\alpha_1+\dots+\alpha_q=1$. Normally we take $\alpha_1=\dots\alpha_q=1/q$.
  • In moving-average model, $\hat x_{t}=\mu+\theta_1 \varepsilon_{t-1}+\dots+\theta_q \varepsilon_{t-q}$ where $\varepsilon_t$ is defined as $\varepsilon_t := x_t-\hat x_t$.

Edit 2: As per @amoeba's request, I have checked the most recent 30 questions (out of 134 in total) tagged with the tag, and here is what these questions are about:

  • 7 are about moving average;
  • 16 are about moving-average model;
  • 4 are unclear (could be either moving average or moving-average model);
  • 1 is neither about one nor the other (mis-tagged).

I did not have the energy to go through more questions this time. I even managed to lose two out of $30$ ($7+16+4+1=28=30-2$).

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  • 2
    $\begingroup$ Can you say a little more about the distinction that concerns you? As someone who doesn't work in that area, I can say that my intuition is that MAMs would use MAs such that [MA] could plausibly be an overarching superset that includes both. Could you, say, list the excerpts that you would want to use for the 2 & that distinguish them sufficiently for askers who aren't all that familiar w/ the topics they are asking about? $\endgroup$ – gung - Reinstate Monica Sep 14 '17 at 16:43
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    $\begingroup$ Would/should [moving-average-model] be a synonym of [arma]->[arima]? That's the ma part, right? Do we have a tag for the ar part? $\endgroup$ – amoeba says Reinstate Monica Sep 14 '17 at 16:43
  • $\begingroup$ I should note that it seems I edited the excerpt some time ago for simplicity / brevity. So the reason the excerpt & the wiki are inconsistent could be my fault. $\endgroup$ – gung - Reinstate Monica Sep 14 '17 at 16:53
  • $\begingroup$ I'm afraid that people would still stick to the shorter MA tag and this wouldn't change much... $\endgroup$ – Tim Sep 14 '17 at 18:07
  • $\begingroup$ @Tim, you might be right. This is precisely why I suggest to include a warning on the use of tags in their excerpts. In any case, a high-rep user or a moderator can change the tag when used inappropriately. But now there is no choice as there is only one tag that hides two quite different objects under it, which causes confusion. $\endgroup$ – Richard Hardy Sep 14 '17 at 19:07
  • $\begingroup$ RichardHardy you are right, but let's imagine that lots of people just stick to the shorter tag. Then you want to search for a question about MAM by filtering by tag and you wouldn't see many of the questions incorrectly labeled as MA. Please notice that moderators and high-rep users won't be able to re-tag all of them. I guess that the ambiguous MA tag is a safer option. Moreover I agree with @amoeba that [arima] tag seems to be OK for it, plus less ambiguous. $\endgroup$ – Tim Sep 14 '17 at 19:29
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    $\begingroup$ @Tim, I see your point. Perhaps then retag the questions related to the moving average model with the arima tag and change the tag description for moving-average to explicitly ban the moving average model from it. $\endgroup$ – Richard Hardy Sep 14 '17 at 19:41
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    $\begingroup$ @amoeba, we have a tag autoregressive which is used for the AR part. $\endgroup$ – Richard Hardy Sep 15 '17 at 5:15
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    $\begingroup$ I reconsidered my comment, what about having moving-average-filter and moving-average-model? $\endgroup$ – Firebug Sep 15 '17 at 22:23
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    $\begingroup$ If we reach consensus about moving on to disambiguate this tag, then, are you willing to step forward and do the job? I suggest you make this clear in the question, because it was common people to suggest tag reorganizations here, but do nothing further when it was time to take actions (that was before @amoeba era; now I believe we should keep the spirit where the asker holds protagonism until the issue is solved). $\endgroup$ – Andre Silva Sep 16 '17 at 12:22
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    $\begingroup$ I just want to say that I am not a big fan of having tag names [foo] and [foo-bar], i.e. when one tag's name is an extension of another. I think this is potentially confusing. It's much better to have [foo-bar] and [foo-schmar], then these two tags will not get mixed up. In this sense @Firebug's suggestion with [moving-average-model] and [moving-average-filter] makes sense to me. $\endgroup$ – amoeba says Reinstate Monica Sep 18 '17 at 11:33
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    $\begingroup$ @amoeba, I agree with the logic of bars and schmars, but I am not sure if moving average filter will be understood as moving average or moving average model or yet another way. When I see moving average filter, I do not know what to think of. $\endgroup$ – Richard Hardy Sep 18 '17 at 12:06
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    $\begingroup$ @RichardHardy Reading a bit it seems so, but it's much less known as that compared to moving averages. Perhaps I've not been hanging out too much with econometrists haha. I think we can make it work with [moving-average] then making ample mention to running/rolling average and the distinctiveness of the MA(q) models. $\endgroup$ – Firebug Sep 18 '17 at 12:59
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    $\begingroup$ @RichardHardy, there usually aren't a lot of votes on tag-related topics; this might be what you can realistically expect to get. It's fine with me either way. $\endgroup$ – gung - Reinstate Monica Sep 26 '17 at 13:53
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    $\begingroup$ @Tim, I would second gung here. Also, leaving the mess as is is a worse option than picking a suboptimal remedy, since, say, the currently-most upvoted remedy is not really controversial, IMHO. We can wait for some more time, but ultimately lack of votes on the best solution does not outweigh the severity of the problem (10 upvotes on the question). Therefore, going with the currently best option makes more sense to me than staying idle. $\endgroup$ – Richard Hardy Sep 26 '17 at 14:13
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Let us keep moving-average for moving average and retag questions about moving-average model (MA(q) model) as moving-average-model, and make nice Wiki excerpts warning not to confuse one with the other.

Pros:

  • Tag names reflect the underlying objects precisely.

Cons:

  • One tag name is an extension of the other, thus adding some confusion.
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  • $\begingroup$ It's been almost a month. I think you can go ahead (if you still want). $\endgroup$ – amoeba says Reinstate Monica Oct 13 '17 at 7:29
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    $\begingroup$ @amoeba, I think I will once I find time. It is a busy period for me right now. $\endgroup$ – Richard Hardy Oct 17 '17 at 6:24
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This is a tweak / combination of two of @RichardHardy's answers here and here.

Let us keep moving-average for moving average (and include a warning about its use in the Wiki excerpt) and retag questions about moving-average model (MA(q) model) as arima.

In addition, we can create a new tag, [moving-average-model], that will be made a synonym of [arima]. An appropriate excerpt will need to be written for this tag. Once it is made a synonym, anyone who uses it will have it automatically replaced by [arima]. Note that there will have to be at least one question that remains tagged with mam so that the tag and its excerpt continues to show up when people type tag suggestions on questions. Moreover, mam and arima would not be merged. The point of leaving mapped tags unmerged is that the tag is more salient when someone searches on, say, "movi". If the tags are merged, they will see "[moving-average] [arima]" as their options, and unless they read very carefully, and understand that a moving-average model is actually a special case of an ARIMA model, they would naturally choose [moving-average] incorrectly. However, if the tags are not merged, [moving-average-model] will show up with its distinctive excerpt. To further clarify how what people will see can differ, consider these two screenshots searching for a merged tag or a tag that is only a synonym:

Merged ("residual-analysis" is not very noticeable, and its excerpt is gone):

merged

Marked as synonym, but unmerged ("[dataframe]" is very salient; its excerpt is prominent; but it will silently be replaced by [r] if it is selected nonetheless):

unmerged

Pros:

  • Tag names reflect the underlying objects precisely.

Cons:

  • One tag name is an extension of the other, thus adding some confusion.
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  • $\begingroup$ Moreover, mam and arima would not be merged. Why? $\endgroup$ – Andre Silva Sep 22 '17 at 20:55
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    $\begingroup$ If [mam] is merged into [arima], then when somebody types "moving-average-mod..." they will get [arima] suggested with [mam] listed below as a synonym. Also, we could modify/expand [arima]'s excerpt to reflect that it can be used for MA. Thus, I am not sure if there is any benefit in leaving it unmerged. $\endgroup$ – amoeba says Reinstate Monica Sep 22 '17 at 21:14
  • $\begingroup$ The benefit is that it is considerably more salient. Moreover, only 1 tag needs to have mam, so w/ a savvy choice (say, this), it could be maintained while minimizing the problems that typically make merging necessary. $\endgroup$ – gung - Reinstate Monica Sep 23 '17 at 0:16
  • $\begingroup$ @gung, +1, I like this option. $\endgroup$ – Richard Hardy Sep 23 '17 at 7:25
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    $\begingroup$ I see your point @gung, but purposefully keeping 1 thread with a synonymized tag is, to me, somehow deeply unsatisfying. It's not how the system is supposed to work; it's a hack. Personally, I would be much more willing to tolerate any disadvantages of the full merge (that you pointed out) than to tolerate this hack. $\endgroup$ – amoeba says Reinstate Monica Sep 23 '17 at 18:35
  • $\begingroup$ It isn't how the system is supposed to work, @amoeba; it is a hack. That said, I don't see any real problem other than violating some idealization of how the system should function. If you want the threads merged, in essence, you want this answer. I was under the impression you were against that. $\endgroup$ – gung - Reinstate Monica Sep 23 '17 at 22:02
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    $\begingroup$ These tags are entirely outside of my expertise or interest, so I don't have much of an opinion. It looks like MA threads should be taken out of [moving-average] tag and retagged as [moving-average-model]. Whether this tag should then remain separate or whether it should be synonymized with [arima], I don't know. But if it is synonymized, then I would prefer a complete merge. $\endgroup$ – amoeba says Reinstate Monica Sep 23 '17 at 22:11
  • $\begingroup$ There is still the [bar] / [shmar] issue w/ leaving MA as one of the tags, @RichardHardy. I grasp, I suppose, your concern w/ using MA-filter, I wonder if it would be better to create a [rolling-average] tag & map MA to that. The only issue here is that when someone searches on "movi", it wouldn't show up. To deal w/ that, I could also create a simple [moving] tag that would be merged w/ RA. As discussed in my answer above, moving wouldn't be very salient, but it would make the new RA tag show up any time someone searches for "movi". $\endgroup$ – gung - Reinstate Monica Jun 8 '18 at 16:04
-1
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Let us keep moving-average for moving average (and include a warning about its use in the Wiki excerpt) and retag questions about moving-average model (MA(q) model) as arima.

Pros:

  • One tag name is not an extension of the other, thus limiting the confusion.

Cons:

  • No separate tag for moving-average model (unlike autoregression).
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  • $\begingroup$ I would vote for this one, but I cannot vote on my own post... $\endgroup$ – Richard Hardy Sep 18 '17 at 12:20
  • $\begingroup$ MA(q) is not necessarily part of a ARIMA framework, even though ARIMA is it's generalization. That would be the same as re-tagging everything AR(p) to ARIMA as well. $\endgroup$ – Firebug Sep 18 '17 at 13:01
  • $\begingroup$ @Firebug, regarding AR(p), I agree, and that is what I have listed under Cons. But I wonder how MA(q) is not part of ARIMA framework? AFAIK, it is a proper subclass of ARIMA. Is there something about "MA(q) proper" that can be contrasted to "MA(q) under ARIMA"? $\endgroup$ – Richard Hardy Sep 18 '17 at 13:23
  • $\begingroup$ Not. Just like AR(p) is ARIMA(p,0,0), MA(q) is ARIMA(0,0,q). $\endgroup$ – Firebug Sep 18 '17 at 14:47
  • $\begingroup$ Richard, could you estimate how many out of 130 Qs currently tagged with [moving-average] are about moving average as such and how many are about MA model? $\endgroup$ – amoeba says Reinstate Monica Sep 20 '17 at 11:53
  • $\begingroup$ @amoeba, sure, no problem. I will try not to forget this until I come home from work and have time for it. $\endgroup$ – Richard Hardy Sep 20 '17 at 12:28
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    $\begingroup$ What if we also made a [moving-average-model] tag (w/ appropriate excerpt) & made it a synoym of [arima]? $\endgroup$ – gung - Reinstate Monica Sep 22 '17 at 12:48
  • $\begingroup$ @gung, that could be done, I think it is not a bad option. $\endgroup$ – Richard Hardy Sep 22 '17 at 13:16
  • $\begingroup$ Should we edit this answer? That version seems to me to be the best option. I wonder if @Firebug would think that addresses his concerns, eg. $\endgroup$ – gung - Reinstate Monica Sep 22 '17 at 13:53
  • $\begingroup$ @gung, Would you like to edit it yourself? Then we will not end up lost in translation (of your idea). $\endgroup$ – Richard Hardy Sep 22 '17 at 13:57
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    $\begingroup$ @gung I'm of the opinion that would only make sense if you also made [autoregressive] synonymous with [arima] as well. $\endgroup$ – Firebug Sep 22 '17 at 14:13
  • $\begingroup$ @RichardHardy, what do you think of also making [autoregressive] a synonym? (Bear in mind that I have only a superficial knowledge of these topics.) Would it be better to write up a 4th, distinct answer w/ all of these pieces, instead of editing an answer that others have already commented & voted on? $\endgroup$ – gung - Reinstate Monica Sep 22 '17 at 14:22
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    $\begingroup$ @gung, I think autoregressive models is a large and significant enough subcategory of ARIMA models that it can stay independent. E.g. you cannot use least-squares estimation for MA or ARMA, but you can for AR, which, among other features, makes it a bit special. A fourth answer it could be. $\endgroup$ – Richard Hardy Sep 22 '17 at 15:23
  • $\begingroup$ See if I captured the ideas faithfully, @RichardHardy. $\endgroup$ – gung - Reinstate Monica Sep 22 '17 at 19:56
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Let us split moving-average into moving-average-filter and moving-average-model and make nice Wiki excerpts warning not to confuse one with the other.

Pros:

  • One tag name is not an extension of the other, thus limiting the confusion.

Cons:

  • The notion of moving-average filter may be unclear (although once the tag excerpt is read, it will hopefully be clear).
  • Moving-average model itself is a filter just like moving average, although perhaps less known. Thus moving-average filter retains the ambiguity of the current moving-average tag.
  • The old moving-average tag can be reintroduced unless blacklisted, which is hard to achieve.
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