Practical guide to using Kendall’s τ in the context of forecasting critical transitions

Recent studies demonstrate that trends in indicators extracted from
measured time series can indicate approaching to an impending transition.
Kendall’s τ coefficient is often used to study the trend of statistics
related to the critical slowing down phenomenon and other methods to
forecast critical transitions. Because statistics are estimated from time
series, the values of Kendall’sτare affected by parameters such as window
size, sample rate and length of the time series, resulting in challenges
and uncertainties in interpreting results. In this study, we examine the
effects of different parameters on the distribution of the trend obtained
from Kendall’s τ, and provide insights into how to choose these
parameters. We also suggest the use of the non-parametric Mann-Kendall
test to evaluate the significance of a Kendall’sτvalue. The non-parametric
test is computationally much faster compared to the traditional parametric
ARMA test.