I was reading the book of Hamilton, time series analysis. I don't understand why in passage $4.2.3$ he expands the geometric serie with alternate signs. Shouldn't the expansion be done only with positive signs?
2026-03-28 08:27:59.1774686479
Prediction of a MA(1) process
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Please take into account that the series development in which all signs of the expansion are positive corresponds to $\frac{1}{(1-\theta)}$, so in this case the expansion is on $\frac{1}{(1-(-\theta))}$ and thus the alternate signs corresponding to $(-\theta)^i$