How is ARMA/ARIMA related to mixed effects modeling? In panel data analysis, I have used multi-level models with random/mixed effects to deal with auto-correlation issues (i.e., observations are clustered within individuals over time) with other parameters added to adjust for some specification of time and shocks of interest. ARMA/ARIMA seem designed to address similar issues.
The resources I've found online discuss either times series (ARMA/ARIMA) or mixed effect models but beyond being build on regression, I don't understand the relationship between the two.  Might one want to use ARMA/ARIMA from within a multilevel model? Is there a sense in which the two are equivalent or redundant?
Answers or pointers to resources that discuss this would be great.
 A: ARMA/ARIMA are univariate models that optimize how to use the past of a single series to predict that single series. One can augment these models with empirically identified Intervention Variables such as Pulses, Level Shifts , Seasonal Pulses and Local Time Trends BUT they are still fundamentally non-causal as no user-suggested input series are in place. The multivariate extension of these models is call XARMAX or more generally Transfer Function Models which use PDL/ADL structures on the inputs and employ any needed ARMA/ARIMA structure on the remainder. These models can also be robustified by incorporating empirically identifiable deterministic inputs. Thus both of these models can be considered Applications to longitudinal (repeated measures) data. Now the Wikipedia article on multi-level models refers to their application to time series/longitudinal data by assuming certain primitive/trivial i.e. non-analytical structures like "The simplest models assume that the effect of time is linear. Polynomial models can be specified to allow for quadratic or cubic effects of time".
One can extend the Transfer Function model to cover multiple groups thus evolving to Pooled Cross-section time series analysis where the appropriate structure (lags/leads) can be used in conjunction with ARIMA structure to form both local models and an overall model.
A: I think the simplest way to look at it is to note that ARMA and similar models are designed to do different things than multi-level models, and use different data.
Time series analysis usually has long time series (possibly of hundreds or even thousands of time points) and the primary goal is to look at how a single variable changes over time. There are sophisticated methods to deal with many problems - not just autocorrelation, but seasonality and other periodic changes and so on.
Multilevel models are extensions from regression. They usually have relatively few time points (although they can have many) and the primary goal is to examine the relationship between a dependent variable and several independent variables. These models are not as good at dealing with complex relationships between a variable and time, partly because they usually have fewer time points (it's hard to look at seasonality if you don't have multiple data for each season). 
