Heteroskedasticity

What is 'Heteroskedasticity'

Heteroskedasticity, in statistics, is when the standard deviations of a variable, monitored over a specific amount of time, are nonconstant. Heteroskedasticity often arises in two forms: conditional and unconditional. Conditional heteroskedasticity identifies nonconstant volatility when future periods of high and low volatility cannot be identified. Unconditional heteroskedasticity is used when futures periods of high and low volatility can be identified.

BREAKING DOWN 'Heteroskedasticity'

In finance, conditional heteroskedasticity is often seen in the prices of stocks and bonds. The level of volatility of these equities cannot be predicted over any period of time. Unconditional heteroskedasticity can be used when discussing variables that have identifiable seasonal variability, such as electricity usage.

As it relates to statistics, heteroskedasticity, also spelled heteroscedasticity, refers to the error variance, or dependence of scatter, within a minimum of one independent variable within a particular sample. These variations can be used to calculate the margin of error between data sets, such as expected results and actual results, as it provides a measure for the deviation of data points from the mean value.

For a dataset to be considered relevant, the majority of the data points must be within a particular number of standard deviations from the mean as described by Chebyshev’s theorem, also known as Chebyshev’s inequality. This provides guidelines regarding the probability of a random variable differing from the mean. Based on the number of standard deviations specified, a random variable has a particular probability of existing within those points. For example, it may be required that a range of two standard deviations contain at least 75% of the data points to be considered valid. A common cause of variances outside the minimum requirement are often attributed to issues of data quality.

Unconditional Heteroskedasticity

Unconditional heteroskedasticity is predictable, and most often relates to variables that are cyclical by nature. This can include higher retail sales reported during the traditional holiday shopping period, or the increase in air conditioner repair calls during warmer months.

Changes within the variance can be tied directly to the occurrence of particular events or predictive markers if the shifts are not traditionally seasonal. This can be related to an increase in smartphone sales with the release of a new model as the activity is cyclical based on the event but not necessarily determined by the season.

Conditional Heteroskedasticity

Conditional heteroskedasticity is not predictable by nature. There is no telltale sign that leads analysts to believe data will become more or less scattered at any point in time. Often, financial products are considered subject to conditional heteroskedasticity as not all changes can be attributed to specific events or seasonal changes.

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