most data sources have many dimensions (for example, energy consumption, temperature, humidity etc.) as well as categorical data like current state (On, Off). The situation is even more difficult if the data is not a regular time series but is more like asynchronous event stream. It would be interesting to find a good forecasting model for some of these use cases.

I'm guessing you already know about this based on the way you described the situation, but the Hyndman Forecasting book [1] discusses various models at length for doing multivariate forecasting models. It's loaded with code and samples in R.

1. https://www.otexts.org/fpp