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Non overlapping periods would make for a far smaller sample


It is due to parameter variation. By overlapping portfolios they can better show that their results are not a one-off result that only works given this very specific set of inputs. Without testing with different parameters (stocks, timeframe, etc), results are liable to blow up given a different input. That is not to say using parameter variation always ...


After some careful thought, the answer is trivially simple, actually. If $\phi_1=0$ then consumption growth is iid. If If $\phi_1=1$ then consumption growth is has a unit root and is not stationary, and so will be the model.

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