If I have $n$ measured and interdependent time series $M_1, M_2, M_3…, M_n$ and have $n-1$ forecast time series $P_1, P_2, P_3…, P_{n-1}$, how can I predict the last forecast time series $P_n$?
Background: Me and some friends are avid river swimmers and we would like to forecast the water temperature. I have logged the past water temperature along with air temperature, wind conditions and solar radiation for the last couple of years. I also have access to the forecast of all these other parameters.
What I know so far is to filter out seasonality by only operating on the difference from the averages of the historical measurements.
But I lack the the mathematical knowledge to now generate a model which predicts the last time series. Can you give me some indication on what is left to do?
The result is ideally a model which given the past data, current conditions and other parameters forecasts for a given time in the future, gives me the water temperature for this point in the future.
Best Answer
If you want to forecast one time series (water temperature) based not only on its previous values but also on another time series (eg air temperature), you should try linear regression with ARIMA errors. Here is a good start: https://www.otexts.org/fpp/9/1