How do you calculate unconditional variance?

How do you calculate unconditional variance?

In finance, risk is usually approximated using the second moment (ie the variance). Similarly that for the mean process, we are able to estimate the unconditional variance of our return serie using a simple variance formula σ2=Var(rt).

What is the conditional variance of Y given that X X?

Similar to the conditional expectation, we can define the conditional variance of X, Var(X|Y=y), which is the variance of X in the conditional space where we know Y=y. If we let μX|Y(y)=E[X|Y=y], then Var(X|Y=y)=E[(X−μX|Y(y))2|Y=y]=∑xi∈RX(xi−μX|Y(y))2PX|Y(xi)=E[X2|Y=y]−μX|Y(y)2.

What is the variance of Y given X?

The conditional variance is similar to the conditional expectation. Var(X |Y = y) is the variance of X, when Y is fixed at the value Y = y. Var(X |Y ) is a random variable, giving the variance of X when Y is fixed at a value to be selected randomly.

What is expectation of variance?

2.3. Expectation and Variance. Given a random variable, we often compute the expectation and variance, two important summary statistics. The expectation describes the average value and the variance describes the spread (amount of variability) around the expectation.

Are ARCH models stationary?

ARCH/GARCH models are also stationary if they satisfy certain conditions similar to the requirements. The stationary requirement is a property of the unconditional distribution of the variance. To answer your question you can model a stationary series with ARMA(p,q) with GARCH residuals.

How to calculate the conditional variance of X?

We previously determined that the conditional distribution of Y given X is: Therefore, we can use it, that is, h ( y | x), and the formula for the conditional variance of X given X = x to calculate the conditional variance of X given X = 0. It is:

How are unconditional and conditional variances collected in a matrix?

Just as the unconditional variances and covariances can be collected into a variance-covariance matrix Σ, the conditional variances and covariances can be collected into a conditional variance-covariance matrix: Note!

Which is the conditional mean of Y given x = x?

Then the conditional variance of Y given that X = x is Because Y is random, so is ( Y − μ Y.x) 2 and hence ( Y − μ Y.x) 2 has a conditional mean. This can be interpreted as the variance of Y given a sample from the subpopulation where X = x.

What is the conditional variance in econometrics called?

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.