# Is a “cycle” always ending where it started?

I am involved in an engineering project. We concern ourselves with a manufacturing process in which mechanical parts are processed. Every time a part is processed we get a set of time series data. A time series is something specific in data science:

A time series is a series of data points indexed (or listed or graphed) in time order. Most commonly, a time series is a sequence taken at successive equally spaced points in time. Thus it is a sequence of discrete-time data. Examples of time series are heights of ocean tides, counts of sunspots, and the daily closing value of the Dow Jones Industrial Average.

Let's say a part is produced in 5 seconds and we get temperature and torque with a rate of 1000 per second. So every Millisecond we write down the time (called timestamp) and the value and we do this for temperature and torque. Thus we get for each part two "lists" of time-value-pairs. Our system is not so exact so we cannot match up the time stamps exactly for both temperature and torque, but that does not matter. Each of these lists is called a "time series" and for each time series we get about 5000 data entries (time-value-pairs). So for each processed part we have this data object which consists out of two time series. I am looking for a word for this data object.

Thus I am looking for a word for "multiple time series that belong together".

Sure, there is a mayor series of processed parts, where the parts are the elements of this series, but I am not concerned with that series.

So in total we have a series of "word" that consists out of multiple time series.

On wiktionary I found "cycle", which apparently is "An interval of space or time in which one set of events or phenomena is completed." The description sounds very promising, but I got the feeling that cycle needs to be something where the end kind of is the end. Am I wrong and should use the word "cycle" or is there a better word?

I don't think there is a specialised term for what I am looking for, so I just want to know: Is a "cycle" always ending where it started?

## migrated from english.stackexchange.comSep 12 '17 at 9:55

This question came from our site for linguists, etymologists, and serious English language enthusiasts.

• I'd say that the cycle is the thing that generates the data, not the data itself. You could call it a "series of data sets". – Max Williams Sep 12 '17 at 8:15
• No: you get one set of data for every part, and each part is produced in a series of producing them. So you get a series of data sets. – Andrew Leach Sep 12 '17 at 8:18
• I'm afraid I don't think that's clear at all. Do you mean "processed" rather than "processes", for a start? I think it would be better if you did not use the term "time series data" without actually explaining what that means, as we are not [generally] mechanical engineers. I have a feeling that your use of "series" is specialised. Series would normally indicate the major series (the complete set of data pertaining to each part, in turn), rather than the different types of data you obtain on each part. – Andrew Leach Sep 12 '17 at 8:27
• So basically it doesn't matter that each part is produced every five seconds: that interval is immaterial. You are measuring each part to produce two time series, and you want a word which groups these two series together, to link them to their processed part. I'm wondering if this would be better asked on a data-science site like Cross Validated, because if there is a particular specialised term, they may well know exactly what it is. – Andrew Leach Sep 12 '17 at 8:52
• @AndrewLeach: The time difference between parts processed may vary, it takes about 5 seconds to process one. But there may be time gaps in processing. On an assembly line you cannot process one after the other without a time gap. E.g. you need to get your robots back into starting position. – Make42 Sep 12 '17 at 8:57

You have two time series, i.e. two random variables indexed by time. If they co-exist together, e.g. in form of list entries (time, temperature, torque), they form together a multivariate time-series.

As about "cycles", you can check which of the following definitions fits your data the best:

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. Hence, seasonal time series are sometimes called periodic time series.

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. Think of business cycles which usually last several years, but where the length of the current cycle is unknown beforehand.

• The timestamps are not always exactly the same, so I wouldn't say it's multivariate time-series. – Make42 Sep 12 '17 at 10:27
• @Make42 but you consider them together right? If so, they are multivariate. The problem is of technical nature: that you have missing data for either of the values at some time points (or even all of them). This can be solved in many ways, e.g. by "rounding" your time intervals, or by predicting the missing data based on the available data and filling it. Nonetheless, it is multivariate (but complicated). – Tim Sep 12 '17 at 10:32
• I see it the same way. For a paper, I would write "multivariate time series" and would dismiss the different time stamps as system errors (which they are), but for programming and talking to stakeholders "multivariate time series" is a mouthful and will lead to confusion. – Make42 Sep 12 '17 at 10:40
• I read your definitions and the blog entry, I think "cycle" applies, even though here we deal with seconds instead of years: The interval length non-fixed (could be 5 seconds, could be 7 or 9) and it does not depend on what day it is or anything like that (as in seasonal). Also, we see a ramp up phase and a ramp down phase and stuff like that during the process, each time. Do you agree? – Make42 Sep 12 '17 at 10:40
• @Make42 yes, years is just an example in the definitions. As about multivariate time-series, you can always give them a definition that by multivariate time-series you mean "multiple time series of related events, hence they are multivariate". – Tim Sep 12 '17 at 10:45