multilevel time series?

Many thanks to both of you. However, I realise now that my description of the data was misleading. When I said "each observed about 15 or 16 times over about a 30-year period", I was referring to *states*, not individuals. So each individual survey respondent appears only once in the dataset, but the states from which samples of respondents are drawn are observed multiple times. (Conceivably, a given person might be sampled more than once, but if that occurs at all it will be extremely rare, and the dataset we have won't tell us this anyway.)

However, your answers/suggestions have, actually, been very interesting, and useful. Consider:

The models we were using looked like:
lmer(outcome ~ covariates + time + (1 | stateyear) + (1 | state), data=data) # time is a linear effect, measured in (whole) years from the earliest year in the dataset

If I understand correctly, Thierry suggests:
lmer(outcome ~ covariates + (1 | stateyear) + (1 | state) + (1 | time), data=data)

I tried this, and the variance at the time level is small, but not zero, implying there are some year-specific disturbances that are common across states. I also got similar results from:
lmer(outcome ~ covariates + time + (1 | stateyear) + (1 | state) + (1 | time), data=data) # time as *both* a linear fixed effect and a random effect

However Doug seems to suggest:
lmer(outcome ~ covariates + time + (1 | stateyear) + (time | state), data=data) # and maybe also with a fixed effect and random slope for time^2

Both suggestions seem reasonable to me, and in fact I ran a model combining them, and got sensible results:
lmer(outcome ~ covariates + time + (1 | stateyear) + (time | state) + (1 | time), data=data)

My co-author and I are satisfied with this, but our reviewer implied he/she wanted to see the model with an AR1 structure, and we're stumped about how to do this. The nlme package can include AR1, but only where the autocorrelation is across lowest-level units, and in our case the autocorrelation is across higher-level units.

Doug, can you suggest a reference that we might use to justify our choice of model? (That, is assuming you still agree with what we're doing, given the revised description of the data, provided above.)

The suggestions are very much appreciated.
- Malcolm