In reply to Brendan.

Great question. I do not know the answer. You might want to ask at a theoretical discussion site such as CrossValidated.

Like you, I suspect that the sample needs to be long enough to contain 5 or 10 cycles of the data. If you think that a lag of length 1 or 2 will model the series, then probably 20 points would be sufficient. If you intend to use a lag of length 12, then 60 or more points might be better. But I don't know what multiplier is recommended.