<p><em>Moving average</em> and <em>moving-average model</em> are two quite different animals, but they seem to be conflated in the name and the description of the <a href="https://stats.stackexchange.com/questions/tagged/moving-average" class="post-tag" title="show questions tagged &#39;moving-average&#39;" rel="tag">moving-average</a> tag. The excerpt implies <em>moving average</em>, while the full Wiki considers <em>moving-average model</em>, although the description is not quite correct. </p>

<p>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.</p>

<p>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, <code>moving-average</code> and <code>moving-average-model</code>. The Wiki excerpt of each tag would include a warning that there is another similar tag but with quite a different object under it.</p>

<p>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 <a href="https://stats.stackexchange.com/questions/tagged/moving-average" class="post-tag" title="show questions tagged &#39;moving-average&#39;" rel="tag">moving-average</a> tag; one can go over all of them one by one.</p>

<p>Does that sound reasonable? Should we do something else? Or do nothing?</p>

<p><strong>Edit:</strong> The differences between the two are the clearest in a forecasting context. </p>

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

<p><strong>Edit 2:</strong> As per @amoeba's request, I have checked the most recent 30 questions (out of 134 in total) tagged with the <a href="https://stats.stackexchange.com/questions/tagged/moving-average" class="post-tag" title="show questions tagged &#39;moving-average&#39;" rel="tag">moving-average</a> tag, and here is what these questions are about:</p>

<ul>
<li>7 are about <em>moving average</em>;</li>
<li>16 are about <em>moving-average model</em>;</li>
<li>4 are unclear (could be either <em>moving average</em> or <em>moving-average model</em>);</li>
<li>1 is neither about one nor the other (mis-tagged).</li>
</ul>

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