Regression with exponentially-smoothed errors I'm just starting to look into exponential smoothing models. Is there a way to fit a linear regression with exponentially-smoothed errors, similar to the standard technique of fitting a regression with ARMA errors? Or is this generally considered a bad idea?
Of course, I can come up with heuristics, like fit with AR(1) errors, then exp-smooth the residuals (possibly on the differences, then look for a trend) but that feels very ad hoc.
 A: What you want to do is to investigate Transfer Function Models ( also known as Dynamic Regression ) which seamlessly integrates "regression" and "arima" . If you were to assume that the arima portion was a simple exponential smoothing model AND the regression component to be a simple contemporaneous relationship you would have your objective. This of course could be silly as you are assuming the model structure. In general you would want to identify the best of these components making sure that pulses, level shifts , seasonal pulses and local time trends were included when necessary. Additionally care should be taken to ensure that the model parameters and errror variance are "proven" to be constant over time. If you had some real data we could take this discussion further.
A: If you're thinking mainly about an EW version of an MA model, I'm not sure why this would be necessary. In general MA models are more of a pain to estimate since they rely on MLE. Oftentimes, people would just throw in sufficient lags in an AR model to cover the MA structure. If the worry is about fitting a particular PACF structure, then it might be appropriate to estimate fractionally integrated models.
A: It is perfectly reasonable to model the residuals of a regression model as a stationary ARMA model.  This is done with harmonic regression. Exponential smoothing is IMA(1,1).  So it would imply nonstationary residuals from the regression. 
