Our tag description for heteroskedasticity says

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.

(Emphasis is mine.)

Q1: What does along some continuum mean here? I wonder if this could be rephrased in simpler terms without altering the meaning.
Q2: How does unconditional heteroskedasticity fit this description? It seems that the description requires conditioning on the continuum, and the examples given are these of conditional heteroskedasticity where the conditioning is w.r.t. one or more predictors or the time index.

  • $\begingroup$ I'd agree that this seems somewhat strange. You could have, say, more variance among men than among women, and many people do not see a continuum of possibilities between these two groups (although surely some do; not that I'd want to start a discussion here :-)). $\endgroup$ – Christoph Hanck Dec 2 '20 at 16:14
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    $\begingroup$ "Along some continuum" is far too restrictive to be appropriate. But I don't understand what you mean by "unconditional heteroscedasticity:" could you explain? $\endgroup$ – whuber Dec 2 '20 at 16:17
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    $\begingroup$ @whuber, I actually had a question about that, posted as a comment elsewhere (for the time being). It reads: [H]ow can heteroskedasticity be unconditional? It seems that the very definition requires conditioning. E.g. our tag definition says "Heteroscedasticity refers to the property of a random process that has non-constant variance along some continuum where it seems the conditioning is done w.r.t. this continuum". Would you say heteroskedasticity is always conditional? Or to phrase it another way, that heteroskedasticity implies conditioning on something w.r.t. which the variance varies? $\endgroup$ – Richard Hardy Dec 2 '20 at 16:37
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    $\begingroup$ "Conditioning" in the probabilistic sense is not required. Heteroscedasticity literally means "different amounts of scatter." It applies purely descriptively to data, for instance, where one subgroup of data may have a strikingly different spread than another (disjoint) subgroup. It may apply to time series (where it is a particular kind of failure of weak second order stationarity). But the general sense of it is that scatter varies, meaning it depends on something, and in that respect the adjective "unconditional" looks like an oxymoron. $\endgroup$ – whuber Dec 2 '20 at 17:05
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    $\begingroup$ Related question: "Terminology: unconditional heteroskedasticity". $\endgroup$ – Richard Hardy Dec 2 '20 at 19:02

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