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There are lot of articles out there that talks about why extrapolation is a bad thing to do.
My question is if the above is true , how are forecasting methods like forecasting the trend based on some time series statistically significant at all ?
Could someone explain why we still use forecasting techniques like regression , ARIMA knowing that we shouldn't extrapolate?
or "all models are wrong, some models are useful." When they say extrapolation is dangerous they are talking about cross sectional regression not time series. There are dangers when you estimate outside the range of your data. But if you don't want to extrapolate you can't do time series at all so its a meaningless point (well for those who do times series to predict the future, others use it for existing data notably in economics). One should not confuse the assumptions and purpose of cross sectional analysis with time series. When you say say something is "statistically significant" you are really saying would what I find in this sample apply outside the sample to the population. That is not what you are doing in time series where there is no sample or population (you are predicting something that does not yet exist). I don't think most who do time series to predict worry if its statistically meaningful or not and few pay attention to regression assumptions generally. They worry if the prediction will be correct.
