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What is a residual in forecasting and what does it tell me?
A residual is the difference between an actual value and what the model fitted or predicted for it, so it is the part the model left unexplained. Studying residuals shows whether the model is missing a pattern, such as seasonality, an event or a trend, and whether its errors are random or systematic.
If a model is capturing everything useful, residuals should look like random noise: centred on zero, without patterns over time and without links to inputs. Visible structure, such as regular spikes each December or errors growing with volume, signals something the model has missed.
Residuals also help spot data errors and outliers, and they underpin prediction intervals. The Japanese word 残差 (zansa), which gives Zansa its name, means exactly this: the residual, what remains after the model.
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