Searching for cycle and time-series I receive 339 results. Cycles are an important pattern in time-series analysis and therefore I think that they should receive their proper tag.

Edit: The difference between a cycle and a seasonality is that a seasonality always appears after the same time period. One example is that Christmas always appears once a year in December. Also every Sunday Christians celebrate Sunday. However a cycle appears in irregular time periods, e.g., business cycles where recession appears more or less twice a decade are an example.

See also here:

A seasonal pattern exists when a series is influenced by seasonal factors (e.g., the quarter of the year, the month, or day of the week). Seasonality is always of a fixed and known period.

A cyclic pattern exists when data exhibit rises and falls that are not of fixed period. The duration of these fluctuations is usually of at least 2 years.

@robjhyndman what do you think as an expert in this area?

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    $\begingroup$ I have no idea what "cycle" is supposed to mean in this context. Can you give a link to a Wikipedia article or something similar that defines this term, and ideally suggest a tag wiki excerpt that you have in mind? $\endgroup$ – amoeba Nov 10 '17 at 14:10
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    $\begingroup$ Could you explain what "cycle" would refer to? We already have a "seasonality" tag. $\endgroup$ – whuber Nov 10 '17 at 14:10
  • $\begingroup$ I'd say that it is a similar case as in here: stats.meta.stackexchange.com/questions/4440/… Moreover, if there is 339 threads and until now they didn't need this tag, then why would we create it now (notice that the threads won't be re-tagged)? you can always search for cycle [time-series]. $\endgroup$ – Tim Nov 10 '17 at 14:12
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    $\begingroup$ Well, 339 is a somewhat misleading number; a more appropriate query finds only 100 Qs. However, looking at them I must agree with @whuber that it seems to be all about seasonality. $\endgroup$ – amoeba Nov 10 '17 at 14:17
  • $\begingroup$ I googled "cyclic pattern" and found robjhyndman.com/hyndsight/cyclicts. Can you ping @RobHyndman to join this discussion and share his opinion? $\endgroup$ – amoeba Nov 10 '17 at 14:23
  • $\begingroup$ The quoted definition of "cyclic" is unusually narrow. In mathematics, "cyclic" is often taken as a synonym of periodic, which in time series analysis means--seasonal. $\endgroup$ – whuber Nov 10 '17 at 15:31
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    $\begingroup$ @whuber I'd say it's unusually broad :-) "A cyclic pattern exists when data exhibit rises and falls that are not of fixed period" -- isn't it basically always true?.. $\endgroup$ – amoeba Nov 10 '17 at 15:35
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    $\begingroup$ @Amoeba Somehow I overlooked the "not"! You're absolutely right--this "definition" is so broad as to be almost worthless. It merely distinguishes data that can be fit with curves having three or more local extrema from all other data. $\endgroup$ – whuber Nov 10 '17 at 15:44
  • $\begingroup$ I have little expertise in time series. But this definition of cyclic (periods that are higher & periods that are lower, of irregular duration) sounds like a moving average process to me. Is it different? $\endgroup$ – gung Nov 10 '17 at 15:58
  • $\begingroup$ @gung The moving average process is a process comparable to an autoregressive process, the cycle" is a pattern comparable to *seasonality or a trend $\endgroup$ – Ferdi Nov 10 '17 at 16:00
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    $\begingroup$ As Ferdi writes, there is indeed a distinction between seasonality (which has a fixed length which is typically known a priori) and cycles, which have varying lengths. As Ferdi writes, the most important examples are business cycles, so I'd expect this distinction to be important in Econ.SE. I'm just unsure how often this situation comes up at CV. Ferdi, can you give a few example questions that would get this tag? $\endgroup$ – Stephan Kolassa Nov 12 '17 at 20:18

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