I would recommend that you model Log(Y) instead of Y and if there is a substantial trend you should model the trend and switch to RDSEM where Y = Trend +Yres where Yres(t)=r*Yres(t-1)+e and Trend= a+b*t+c*Exp(t) (or something similar)
To do that kind of model in Mplus you would use Y^ on Y^1; Y on T ExpT; where define: ExpT=Exp(t)
a related question. I calculated a two level DSEM for a time series of about 30 years. The lagged variable was log-transformed beforehand. The model converged, and I looked at the distribution of the individual estimates of phi (my random AR coefficient). About two percent of all 3500 individuals in the sample displayed a random AR coefficient > 1, which I expected.
In Appendix D of your paper (Asparouhov, Hamaker, Muthen, 2018) you said that non-stationarity can yield biased subject-specific mean and variance estimates. Is this the matter only on the individual level, in this case for the 2 percent with AR>1, or does it also influence the average AR estimate for my entire sample in a way that I cannot trust the results anymore?
Hence, my question. At which expected proportion of AR>1 in the random effects should I switch to RDSEM? If I think there might be any person displaying it? Or 2%, 10%, 50% of persons in the sample? I am somewhat confused about what counts as a 'substantial' trend that then needs to be modelled in RDSEM instead of DSEM.
The DIC criterion can be used to compare the RDSEM and DSEM models (and even the standard two-level model when it is setup as DSEM/RDSEM model with AR fixed to 0, see Table 5).
If the trend model doesn't have random effects you can try adding random effects for the trend. Another possibility is to add a quadratic term for trend. You might want to do all that in a two-level setup first (no ar coefficients). We generally try to resolve large AR coefficients. One thing to keep in mind is that sometimes the posterior distribution of the AR coefficient exceeds 1, while the actual point estimate is less than 1 - we don't really consider that a major problem and it does tend to happen fairly often as the models get more flexible and the posterior distributions of the random effects get wider.