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The forecast_fitted_values returns the predictions for the training set exclusively (never into the future). If you use max_horizon=4 for example, then you have 4 models, so each of those 4 models has a slightly different training set (due to targets being offset) and when you compute the fitted values then you get a dataframe with an

h

column which denotes the horizon that model was fit to (1, 2, 3, or 4) in this case.