Moment Component Analysis: An Illustration with International Stock Markets

Abstract

It is well known that non-normality plays an important role in asset and risk management. However, handling a large number of assets has long been a challenge due to the curse of dimensionality. We describe a statistical technique, which we call Moment Component Analysis (MCA), that extends Principal Component Analysis (PCA) to higher moments such as skewness and kurtosis. This method allows us to identify factors that drive co-skewness and co-kurtosis across assets. We illustrate MCA using 44 international stock markets sampled at weekly frequency from 1994 to 2014. We find that both the co-skewness and the co-kurtosis structures can be summarized with a small number of factors. Using a rolling window approach, we show that these co-moments convey useful information about market returns, complementary to the information extracted from a standard PCA.

Keywords: PCA, Skewness, Kurtosis, Portfolio analysis, Tensor, Random Matrix Theory

JEL Classification: G11, G15, C51.