Is ARIMAX(0, 0, 0) OLS? I have been fitting some models to a time series I have and amongst these are an AIRMAX(0, 0, 0) model. I am using the statsmodels implementation of ARIMA(X) in python and have a simple question:

Is an ARIMAX(0, 0, 0) model simply an OLS model?

My interpretation of the sparse documentation is that it is. Can someone confirm this or explain why I am wrong?

ARIMAX(0,0,0) is a model. OLS is an estimation technique. This is an apples-to-oranges comparison.
ARIMA(0,0,0) model for a dependent variable $y_t$ means $y_t=\beta_0+\varepsilon_t$ where $\beta_0$ is a constant and $\varepsilon_t$ is white noise. You do not even need OLS to estimate such a model, as there is not much to estimate. You can obtain  $\beta_0$ as the empirical mean of $y$ and the variance of $\varepsilon_t$ as the empirical variance of $y$.
ARIMAX(0,0,0) could be understood as $y_t=\beta_0+\beta_1 x_t+\varepsilon_t$. This model could be estimated by OLS. (Loosely speaking you could say this is an OLS model, and many people would understand what you intend to express. Yet I suggest keeping a distinction between models and estimation techniques; this may come in handy in some more complicated situations when clear terminology may prevent larger confusion.)
