Which is the correct formula for conditional variance?

Which is the correct formula for conditional variance?

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. Var ⁡ ( Y | X ) = E ⁡ ( ( Y − E ⁡ ( Y ∣ X ) ) 2 ∣ X ) .

Is the variance of X a function of itself?

As a result, itself is a random variable (and is a function of X ). Recall that variance is the expected squared deviation between a random variable (say, Y) and its expected value.

Which is the best interpretation of the definition of variance?

Thus, one interpretation of variance is that it gives the smallest possible expected squared prediction error. If we have the knowledge of another random variable ( X) that we can use to predict Y, we can potentially use this knowledge to reduce the expected squared error.

When do you use conditioning on a random variable?

Conditioning on discrete random variables. When X takes on countable many values with positive probability, i.e., it is a discrete random variable, we can introduce , the conditional variance of Y given that X=x for any x from S as follows: where recall that is the conditional expectation of Z given that X=x,…

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!

How to calculate conditional covariance between Y I and Y J?

Conditional Covariance Let Y i and Y j denote two variables of interest, and let X denote a vector of variables on which we wish to condition. Then the conditional covariance between Y i and Y j given that X = x is σ i, j. x = cov (Y i, Y j | X=x) = E { (Y i − μ Y i.

Which is the conditional variance of [UNK] T?

Note that the conditional variance of ϵ t is equal to σ t 2. However since we know that the variance is time varying we also know that σ t 2 has a time dependent structure and exhibits autocorrelations (so do the squares returns residuals).

How to calculate the conditional variance of a GARCH model?

As far is know the term conditional variances is used only in GARCH models. So, I assume that in order to calculate these variances one has to use a GARCH Model for the returns. First, one has to calculate the returns r t = ln ( p t − 1). Then, the returns should be centered via r ^ t = r t − r ¯ (quite unsure if this meant by centered).

Is the mean and variance of X I the same?

That is, we have shown that the mean of X ¯ is the same as the mean of the individual X i. Let X 1, X 2, …, X n be a random sample of size n from a distribution (population) with mean μ and variance σ 2. What is the variance of X ¯?

What does conditional expectation of y mean in math?

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).