Prediction Loss
Explore the concept of prediction loss in ARIMA time series modeling. Understand how loss functions such as mean squared error, mean absolute error, and root mean squared error help measure forecast accuracy. Learn how prediction errors arise from unknown shocks and how minimizing these loss functions is essential for optimizing model parameters and improving forecasts.
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The ultimate goal of ARIMA models is forecasting and, in particular, point forecasting. Assume that we’ve got a time series
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
Note: We use the hat symbol, ^, to denote parameter estimates ( ...