# what does it mean when a time series cannot be converted to a stationary process?

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?

• What do you mean when you say that the time series is a function of time?
– Dave
Aug 7 at 2:27
• 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. Aug 7 at 3:20