The dominant temporal variability of the leading EOF mode for annual precipitation can essentially be described as a white noise process. (link.springer.com)
However, not all aspects of the time series of the annular modes are consistent with a red - noise process with a 10 day timescale: e.g., the annular modes exhibit enhanced variability on monthly timescales during seasons of rigorous stratosphere / troposphere coupling (see section on Stratosphere / troposphere coupling, below); and both annular modes have exhibited trends over the past few decades towards their high index polarities (see section on Climate Change, below). (atmos.colostate.edu)
That's why everyone does significance testing — which is the issue that M&M were addressing, not that MBH98 detected a «significant» correlation between a stationary noise process and a non-stationary deterministic signal, but that the chance of the algorithm doing so was underestimated. (realclimate.org)