# How to use ARIMA to predict time series?

  Time            Volume
9/30/2019          2000
10/1/2019          1800
10/2/2019          1600
10/3/2019          1400
10/4/2019          1200
10/5/2019          1000
10/6/2019           800
10/7/2019           600
10/8/2019           400
10/9/2019          2000
10/10/2019         1800
10/11/2019         1600
10/12/2019         1400
10/13/2019         1200
10/14/2019         1000
10/15/2019          800
10/16/2019          600


I have this dataset with Volume consumption of a tank over period of time. The volume decreases with time and on 10/9/2019 the tank has a load-up and is full tank. I have data for over a year and would like to use ARIMA to predict when would the next load-up happen based on previous consumptions.

ARIMA models try to capture autocorrelation in your time series in order to make predictions. It is composed of three main models: AR, MA and I. So, you build your model to predict future values based on a linear combination of past values, linear combination of past errors and a differencing term (I) that accounts basically for a trend. You should get more information here: Forecast: Principles and Practice

My question is: why do you believe the tank volume is predicted by its own past values? When you ask how to use ARIMA, it is straight forward, however, I am concerned that you are not think properly about your problem. Isn't there an exogenous variable you could use? Maybe try a different model? A physical one?

If you really want to use ARIMA, you need to check if your data is not a random walk, plot autocorrelation and partial autocorrelation functions to see analyze which coefficients are more appropriate for AR and MA terms. Check for stationarity. Or simply use autoarima although I don't recommend doing that for the first time.