What Is Heteroscedasticity?

Heteroscedasticity is a type of statistical phenomenon where a variable’s variance changes with its mean. This means that there is unequal variability among the values of a single variable. For example, when a variable’s mean and variance increase together, it is considered heteroscedastic. In the business and finance world, heteroscedasticity is the most often found and can result in biased estimates and incorrect inference in regression analysis.

Examples of Heteroscedasticity

One example of heteroscedasticity is when the variance of a stock’s monthly returns increases the higher the stock’s average returns are. In this case, the larger the average returns, the more “risky” the stock is perceived to be.

Another example of heteroscedasticity is when a company’s sales fluctuate around a trend. For example, when a company reorganizes its business to target more affluent consumers, or enters into a new market, its sales might start to increase with each quarter, then eventually level off when the reorganization period has ended.

How to Identify Heteroscedasticity

Heteroscedasticity can be identified in a few different ways. The easiest and most common method is to calculate the residuals of the data. Residuals represent the difference between the observations and their predicted values. If the residuals are increasing in one direction or another, it is a potential indication of heteroscedasticity.

Another method to determine heteroscedasticity is to create a graph to display the variance among the observed values. A scatterplot can be used to examine the variability across the observations, and if the pattern is a shape other than random, then this is an indication that heteroscedasticity may be present.

How to Deal With Heteroscedasticity

Heteroscedasticity is a problem that must be addressed before performing any regression analysis. The most common way to handle heteroscedasticity is to transform the data using a log transformation. This technique reduces the relationship between the mean and variance, eliminating the issue of heteroscedasticity.

Another technique to address heteroscedasticity is to use weighted regression. This technique assigns more weight to the observations with higher variance, thus making the regression less sensitive to any heteroscedasticity present.

Understanding heteroscedasticity and how to identify and deal with it is important in the business and finance world. By recognizing heteroscedasticity and using the appropriate techniques to address it, one can ensure that reliable and accurate outcomes from regression analysis are achieved.