Table 3.

List of candidate early warning signals and their estimating equations. See [15] for details.

EWS	estimator	theoretical correlation with ${\mathcal{R}}_e(t)$ in an emergence scenario
mean	$\overline{y}=\sum _{i=1}^n\frac{y_i}{n}$	positive
variance	$s^2=\sum _{i=1}^n\frac{{(y_i-\overline{y})}^2}{n}$	positive
coefficient of variation	$\frac{s}{\overline{y}}$	null
index of dispersion	$\frac{s^2}{\overline{y}}$	positive
skewness	$\frac{1}{s^3}\sum _{i=1}^n\frac{{(y_i-\overline{y})}^3}{n}$	positive
kurtosis	$\frac{1}{s^4}\sum _{i=1}^n\frac{{(y_i-\overline{y})}^4}{n}$	positive
autocovariance	$s_1^2=\sum _{i=2}^n\frac{(y_i-\overline{y})(y_{i-1}-\overline{y})}{n}$	positive
autocorrelation	$r_1=\frac{s_1^2}{s^2}$	positive