I can't figure out if this time plot has increasing variance or not. From my initial guess of the time plot, I would say no but I've taken the difference and it looks like variance is increasing slightly. I've subsequently taken a log transformation and differenced that also where the variance looks to be constant. I'm just wondering is the data variance increasing so much that a log transformation needs to be taken in order to start making the series stationary? I've attached all plots below. , ,
My eye tells me (marginally!) yes, but I would prefer actually testing for non-constant error variance via the TSAY test discussed here http://docplayer.net/12080848-Outliers-level-shifts-and-variance-changes-in-time-series.html . Note that the error variance can change at different points in time AS COMPARED to the error variance being proportional to the expected value as is discussed here When (and why) should you take the log of a distribution (of numbers)? .
Note well that untreated anomalies can often incorrectly guide the erroneous conclusion that variability of the error process is non-constant which is why Box and Jenkins incorrectly transformed/logged the Airline series. See a discussion here https://autobox.com/cms/index.php/blog and https://autobox.com/pdfs/vegas_ibf_09a.pdf illustrating the spurious correlarion between error variance and the expected value caused by a few anomalies in the most recent year.
Actually post your original observations and I will be more analytical/objective in my assessment of "constant error variance" .