Statistical Traps to Avoid #1: Autocorrelation
Two sine waves. The dashed line is a sine wave with a period of 11 yr, and the solid line is a sine wave with a period of 3.7 yr. The solid circles mark the value of the shorter-period sine curve at the time when the longer-period sine reaches its peak (Haam and Tung 2012).
Eddie Haam and K.K. Tung (2012, J. Atmos. Sci.) examine the purported relationship between the 11-year solar cycle and 2–4-year cycle in La Niña. The authors demonstrate that there is no relationship between these two variables that they have found that is statistically significant. Instead, the autocorrelation between the two quasi-periodic variables is likely to explain the relationship. In other words, the relationship is just a coincidence because of the timings of the two independent quantities are often found at the same points in the cycle.
This is demonstrated by two synthetic time series where the dots indicate that 9 out of 11 peaks in the solar cycle (dashed blue lines) have below-normal values in the ENSO cycle (solid green lines).
Haam, Eddie, Ka-Kit Tung, 2012: Statistics of Solar Cycle–La Niña Connection: Correlation of Two Autocorrelated Time Series. J. Atmos. Sci., 69, 2934–2939.
doi: http://dx.doi.org/10.1175/JAS-D-12-0101.1
