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I want to forecast monthly air traffic of an airport for the next 3 years. I have 20 years (240 months) of monthly historical data.

How do I determine which time period of the historical data should my forecast be based on?

Is there any advantages or disadvantages of using just the past 5 or 10 years of data?

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If there exist structural breaks in your data, which might alter the parameters that produce the data, then you may want to cut out the data before that structural break occurred so that you can forecast with the correct parameters.

If you notice a seasonal pattern 10 years ago that you know has died out, you may also want to cut out that data to simplify modeling.

For example, if it's air traffic you're modeling, you may want to cut out the period before 9-11. Also, I suspect there is an transient intervention in the current period, caused by Covid-19, which will probably mess up forecasts going forward until airport travel stabilizes when (if) the virus passes.

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Since you did not give the exact values, I can't know for sure which time period is better, but I believe you either choose time period depending on seasonal pattern or calculate the forecasting error with the values provided.

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