Conditional variance

In probability theory and statistics, a conditional variance is the variance of a random variable given the value(s) of one or more other variables. Particularly in econometrics, the conditional variance is also known as the scedastic function or skedastic function. Conditional variances are important parts of autoregressive conditional heteroskedasticity (ARCH) models.

The conditional variance of a random variable Y given another random variable X is

The conditional variance tells us how much variance is left if we use ${\displaystyle \operatorname {E} (Y\mid X)}$ to "predict" Y. Here, as usual, ${\displaystyle \operatorname {E} (Y\mid X)}$ stands for the conditional expectation of Y given X, which we may recall, is a random variable itself (a function of X, determined up to probability one). As a result, ${\displaystyle \operatorname {Var} (Y|X)}$ itself is a random variable (and is a function of X).

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