Moments of a Time Series: Skewness and Kurtosis

Motivation

Most exploratory data analyses will go into the mean and variance of a time series one way or another. While these are certainly very important moments, the next two are usually not considered. In this lesson, we’ll look at the third and fourth moments of a distribution: the skewness and the kurtosis. We use these moments to look at the shape of the distribution and, in particular, its tails. By tails, we mean the values on the far sides of the mean. The skewness and kurtosis tell us about the symmetry and the thickness of the tails of our series, respectively.

Skewness

As we’ve just said, skewness is the third moment of a time series distribution. It gives us a measure of how (a)symmetrical its tails are. Skewness is defined as: