Inverse models for dissolved oxygen that simultaneously estimate metabolism and gas exchange in streams and rivers have enabled estimating metabolism for long time series and many places, without the onerous fieldwork needed to independently estimate gas exchange. A core problem with this approach is that parameters may not all be identifiable, such that many combinations of estimates for gas exchange and ecosystem respiration may produce an acceptable fit to the model, but with high uncertainty in, and large covariance among, the metabolic parameters. An overlooked component of these models is the way errors are defined, which should be consistent with properties of the residual variation. Fitting the wrong stochastic component of a model can affect predictions of the metabolism parameters. Many commonly used models, including one many of the coauthors popularized in the package streamMetabolizer, assume normally distributed and independent process error. However, patterns of residual variation often do not meet this assumption. Process error shows strong autocovariance and variation that changes through time within a day. Here we explore use of more complicated time series models for this error term including autoregressive parameters and GARCH structure to account for heteroskedasticity. These approaches can improve model fit and alter estimates of metabolism parameters, but can be difficult to fit. We suggest that there is much room for refining and improving metabolism models.