...

/

Prediction Loss

Prediction Loss

Learn about forecast errors and loss functions.

We'll cover the following...

The ultimate goal of ARIMA models is forecasting and, in particular, point forecasting. Assume that we’ve got a time series yty_t with a total of TT observations. With point forecasting, we aim to get the best possible guess for the value of yty_t, hh steps into the future. That is, we want to predict yT+hy_{T+h}.

Note: In this lesson, we use forecast and prediction interchangeably.

Prediction vs. reality

The logic of ARIMA models is that the past determines the future via some AR and MA structures. Assume that we’ve got a series yty_t that follows a known AR(22) process. To predict yT+1y_{T+1}, for example, we could simply plug the last two realizations of yty_t in the AR(22 ...