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The 13 month moving average would be the average of the last 6 months, the next 6 months and the current month. So it has an advantage of being a better estimator of the current month, with the disadvantage of not being calculable for the last 6 months of the graph (which is obvious in the figure).
A (one-sided) moving average of the previous 12 months will be biased downward if there is an upward trend, since it’s the average of lower lagging months.

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