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What is Heteroskedasticity?

Danielle DeLee
Danielle DeLee

Heteroskedasticity is a statistical term used to describe the behavior of a sample’s variance and standard deviation. If the quality is present, then the variance and standard deviation of the variable are not constant over the entire graph of the sample data. If these measures are constant, then the data is said to be homoskedastic.

The variance of a variable is a measure of how far the observed values are scattered from the mean, or average, value. The standard deviation is the square root of the variance, and it is often used to describe distributions. According to the relationship described by Chebyshev’s theorem, a certain percentage of data must fall within each standard deviation from the mean value. For example, at least 75 percent of the data points in a sample must be within two standard deviations from the mean. Thus, the standard deviation of a sample gives rough information about each data point’s relative position.

Man climbing a rope
Man climbing a rope

There are two varieties of heteroskedasticity: conditional and unconditional. If data is conditionally heteroskedastic, analysts cannot predict when data will be more scattered and when it will be less scattered. This is the case for the prices of financial products, including stocks.

Unconditional heteroskedasticity is predictable. Variables that are cyclical by nature commonly exhibit this property. Variables whose variance changes with their level are also unconditionally hetroskedastic. For example, you can predict that if you can hold something in your hand, you can gauge its weight fairly accurately; you might be, at most, a few pounds or kilograms off. If you are asked to estimate the weight of a building, however, you might be incorrect by thousands of pounds or kilograms — the variance of your guess increases, predictably, with the weight of the object.

Whether or not heteroskedasticity is present has bearing on the proper interpretation of statistical analysis of the data. The quality does not affect regression; this means that methods of placing best-fit graphs will work equally well with both heteroskedastic and homoskedastic data. These graphs are created by finding the coefficients of data, which measure how much a particular variable affects an outcome. Heteroskedasticity skews the values of the coefficients’ variance that the models return.

There are a variety of mathematical tests that can determine whether there is heteroskedasticity present on a sample of a variable. Many of these tests are available in statistics analysis software. An observer can also detect some cases of heteroskedasticity by looking at a graph of the sample. Look for areas of the graph that are scattered more or less; it is important to distinguish, however, between true variations in the amount of scatter and the clusters that are expected in distributions that have an element of randomness.

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