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Two time-series forecast principles are used: a seasonal moving average and a seasonal single exponential smoothing forecast.

To attain quality results, the associated constants (the season size, the number of values included in a moving average forecast and the smoothing constant) are optimized in a grid search. What would be the correct terminology to describe this process? "Hyperparameter optimization"?

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In forecasting, these are not commonly considered hyperparameters, just "plain vanilla" parameters. Just use "parameter optimization".

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