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I am new to forecasting time series. The team that I am working with keep referring to forecasting period as lag. For example we have 20 month of data and we would like to create 5 month forecast. Is it appropriate (industry accepted) to call 5 month forecast as 5 month lag?

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Generally, lag(n) would refer to moving an actual value ahead by n periods. It would be better to call this a 5 month forecast horizon.

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