Disclaimer: I am a new learner when it comes to time series.

Typically, before obtaining summary statistics like the mean, or applying models like ARMA, you would want to transform your time series to a stationary process using differencing or log transforms.

But consider that your time series follows a sigmoid shape. In this case, no amount of differencing will convert the time series to a stationary process. I assume this is because the time series is not resultant of a (potentially latent) continuous random variable with a fixed mean and variance. But rather a variable that is a function of time.

Because of this, you are not able to do any kind of ARMA modeling, or determine summary statistics like the mean.

What happens then? Can you just not do any analysis on it?

  • $\begingroup$ What do you mean when you say that the time series is a function of time? $\endgroup$
    – Dave
    Aug 7 at 2:27
  • $\begingroup$ Say the time series is a participant's perception of pitch in a song. From 0:00-0:30 the song has a low fundamental frequency (f0), and from 0:31-1:00 the song has a high f0. So participant pitch ratings in the low f0 section (0:00-0:30) will be deterministically lower than the high f0 section (0:31-1:00). In this way, the song's pitch can be considered a function of time. The f0 is not considered random, but participant pitch ratings are random. $\endgroup$ Aug 7 at 3:20

It depends on the length of the time series. For instance, if I have only six months of temperature data, then I cannot use an ARIMA model to forecast the other six months, as the data I have so far does not fully pick up the seasonal pattern.

On the other hand, if I have three or four years worth of data, then the seasonal pattern can be more easily detected.

In this regard, I would try expanding the length of your time series to determine the best model. If you are working with only a few minutes of data (as seems to be the case in your comment) then the data simply is not exhaustive enough to infer characteristics of the time series over a longer period.


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