  Recent studies demonstrate that trends in indicators extracted from measured
time series can indicate approaching to an impending transition. Kendall's
{\tau} 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's {\tau} are 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 {\tau}, 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's {\tau} value. The non-parametric test is computationally much faster
compared to the traditional parametric ARMA test.
