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Recent studies demonstrate that trends in indicators extracted from measuredtime series can indicate approaching to an impending transition. Kendall's{\tau} coefficient is often used to study the trend of statistics related tothe critical slowing down phenomenon and other methods to forecast criticaltransitions. Because statistics are estimated from time series, the values ofKendall's {\tau} are affected by parameters such as window size, sample rateand length of the time series, resulting in challenges and uncertainties ininterpreting results. In this study, we examine the effects of differentparameters on the distribution of the trend obtained from Kendall's {\tau}, andprovide insights into how to choose these parameters. We also suggest the useof the non-parametric Mann-Kendall test to evaluate the significance of aKendall's {\tau} value. The non-parametric test is computationally much fastercompared to the traditional parametric ARMA test.

Practical Guide of Using Kendall's {\tau} in the Context of Forecasting Critical Transitions