In which predictive tasks are the ARIMA model useful?
A popular and widely used statistical method for time series forecasting is the ARIMA model. ARIMA is an acronym that stands for AutoRegressive Integrated Moving Average. It is a class of model that captures a suite of different standard temporal structures in time series data. You can read about it more here.

Based on your problem statement, it definitely looks like ARIMA model can help as you are predictions are based of previous time series data. However, as a rule of thumb in Machine learning, there is no one model that can solve the problem out of the box. There is a saying in statistics that goes something like this : 


  All models are wrong, some are useful.


What this implies is, you can start with ARIMA but you need evaluate your model to see if ARIMA can solve the problem for you or you need to explore further.