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Does it ever make sense to treat a time series as not being a time series?

For example, I have a time series of nine years of annual summer averages of zooplankton biomass and cumulative lake inflow.

The researcher who gathered the data suggested that because the behavior of the system in one year does not have any influence on the system in the next year (e.g., very short life cycles of these animals), it doesn't make sense to test for auto-correlation. Both time series are auto-correlated if we assume that it makes sense to think of them as time series.

He wants to determine the correlation between flow and zooplankton, but I think that the correlation and the p-value of the correlation can't be determined without taking into account that the data are essentially pseudo-replicated. There will therefore be fewer degrees of freedom, and the p-value, at least, has to be adjusted to take that into account.

Who's right?

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