Skewness and Kurtosis


In some cases disturbances push the state of the system towards values that are close to the boundary between the two alternative states. Because the dynamics at the boundary become slow, we may observe a rise in the skewness of a time series- the distribution of the values in the time series will become asymmetric. Just like variance, skewness can also increase because of flickering. Skewness is the standardized third moment around the mean of a distribution. Note that skewness may increase, or decrease, depending on whether the transition is towards an alternative state that is larger or smaller than the present state.

Flickering or strong perturbations also make it more likely that the state of a system may reach more extreme values close to a transition. Such effects can lead to a rise in the kurtosis of a time series prior to the transition; the distribution may become ‘leptokurtic’: the tails of the time series distribution become fatter due to the increased presence of rare values in the time series. Kurtosis is the standardized fourth moment around the mean of a distribution.

Ensemble example for rolling window metrics