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View submission: Are snowfall totals independent from one winter to the next?
Multi-year lagged autocorrelation certainly exists. It's just weaker than the single year lagged autocorrelation. I think you're asking if the correlation ever "skips" a year, though, i.e. precipitation for this year is uncorrelated with precipitation from next year, but it is correlated with precipitation two years from now. I am unaware of any climatological process that results in this sort of pattern.
There's nothing here!