Non-constant variance along some continuum in a random process.

Heteroscedasticity refers to the property of a random process that has non-constant variance along some continuum. This most commonly presents in regression where the error variance increases as a function of one or more predictors, but also commonly refers to a time series whose variance changes over time. The Greek skedasis means "dispersion".

Random data showing heteroscedasticity: . . . . . and heteroscedastic vs. homoscedastic residuals:
by Q9. . . . . . . . . . by Protonk.

Heteroscedasticity may be intrinsically interesting, as in this example from Wikipedia:

A classic example of heteroscedasticity is that of income versus expenditure on meals...A poorer person will spend a rather constant amount by always eating inexpensive food; a wealthier person may occasionally buy inexpensive food and at other times eat expensive meals. Those with higher incomes display a greater variability of food consumption. [Emphasis added.]

Heteroscedasticity may complicate predictive/explanatory modeling, as in the other example:

Imagine you are watching a rocket take off nearby and measuring the distance it has traveled once each second. In the first couple of seconds your measurements may be accurate to the nearest centimeter, say. However, 5 minutes later as the rocket recedes into space, the accuracy of your measurements may only be good to 100 m, because of the increased distance, atmospheric distortion and a variety of other factors. The data you collect would exhibit heteroscedasticity. [Emphasis added.]

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