Neural Network Timeseries Modeling with Predictor Variables Many have shown the effectiveness of using neural networks for modeling time series data, and described the transformations required and limitations of such an approach. R's forecast package even implements one approach to this in the nnetar function. 

Based on my reading, all of these approaches are for modeling a single outcome variable based on its past observations, but I'm having trouble finding a description of a neural-network-based approach that also incorporates independent predictor variables (a sort of ARIMAx analogue for neural networks). I've found references to Nonlinear autoregressive exogenous models (NARX), which seem like they should be what I'm looking for, but all the reading I've been able to find talks more about using this approach for multi-step-ahead prediction of a univariate series. 

Can anyone point me in the right direction on this? For bonus points, does anyone know of an implementation of what I'm looking for in R?
I think this thesis https://dspace.mit.edu/bitstream/handle/1721.1/99565/924315586-MIT.pdf?sequence=1 is a good starting point for building a model for time series forecasting with so called leading indicators and different machine learning models. Basically you need just to training sets where your inputs are past values of the variable you wish to predict plus the additional indicators (i.e. past_value_t-6, past_value_t-5 ..., past_value_t-1, additional_variable_1, additional_variable_2, ..., additional_variable_n) and the output is either single value in future (t_1) or multiple values (t_1, t_2, ... t_n), in case you wish to predict for example the next twelve moths' sales.

It is also possible to use recursive strategy to generate future values for your prediction variable. In this case you generate next value for the prediction value based on your previous predicted value. However, at least based on my experience the first mentioned direct strategy is way more efficient.