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I have to forecast the amount of cars sales for the next 12 months. The data I have gathered are from 2013-2021 (108 months). This is what the plot of my data looks like using Rstudio and its function plot.ts(): raw data

We can see the mean and the variance are not constant - so I tried the log, root and Box-Cox transformations and all the graphs I got still remain the same (except, of course, the y-axis). They are all shaped identically and therefore none of my graphs is stationary. Here are what my log and root transformation plots look like:

log transformation

root transformation

What can explain this issue? I tried to look it up online and but couldn't find anything.

baoiba
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    The relative range of your values is so small that it makes little difference which of those transformations you take: they are all designed not to change data that have only a little variation. See https://stats.stackexchange.com/a/467525/919 for details. BTW, it is not at all evident that "mean and variance [are] not constant." Sure, the mean appears to increase a little over time, but what leads you to believe the variance is not constant? – whuber Apr 16 '22 at 22:13
  • @whuber I was asked to gather max 112 observations and to do a data transformation if the variance appears not to be constant - towards the 70th month, it seemed to me that the variance starts to increase... – baoiba Apr 16 '22 at 22:47
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    It's difficult to determine that just from looking at the plot of data. Consider first smoothing the data and examining a plot of the residuals: that will give you a clearer sense of whether the variance changes and how. Yes, there is some indication of more variability at later dates, but it isn't necessarily a change in variance: there appear to be some structural breaks around times 72 and 84 that might be better handled as such. No transformation is going to help you deal with those. See https://stats.stackexchange.com/a/74594/919 for a worked example. – whuber Apr 16 '22 at 23:04

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