If we have 2 ways of predicting a variable y: Regression:
y(t) = ax(t) + b + e;
and a time series AR model:
y(t) = c.y(t - 1) + d.y(t - 2) + e.
And both give similar results in out of sample testing, which method should we choose?
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The regression model assumes the errors to be independent, whereas the time series autorregresive model takes into account the correlation. Maybe the output for some specific forecast is the same but the models are not, and if your data is correlated over time you should take the second approach.