Alternative Methods to Measure Correlation

Nigel Da Costa Lewis

An important element of applied statistical modelling involves examining the relationship between two or more random variables. Take, for example, an analyst who is interested in knowing the relationship between European stock market indexes. The goal may be to assess the relative risk of each index and build a successful trading strategy. If the analyst simply assumes no relationship exists between the indexes, they may be exposed to the risk that they move together in a predictable fashion. In this chapter, the popular metrics for calculating correlation will be compared, the role of hypothesis testing discussed and details on constructing confidence intervals outlined. The chapter ends with a discussion of correlation metrics when the variables of interest are binary rather than continuous. Code samples in R help clarify many of the concepts.

Correlation coefficients provide a way to characterise the close-ness of the indexes over time. It measures the extent to which two variables are related to each other by assuming a linear relationship, and takes values between –1 and +1. A value of –1 indicates a perfectly negative linear relationship and a correlation of +1 indicates a