What is a conditional variance model?

What is a conditional variance model?

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. Conditional variances are important parts of autoregressive conditional heteroskedasticity (ARCH) models.

How do you prove conditional variance?

Conditional Variance: 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 conditional variance in Garch model?

A process, such as the GARCH processes, where the conditional mean is constant but the conditional variance is nonconstant is an example of an uncorrelated but dependent process. The dependence of the conditional variance on the past causes the process to be dependent.

Is covariance the same as conditional variance?

Variance and covariance are mathematical terms frequently used in statistics and probability theory. Variance refers to the spread of a data set around its mean value, while a covariance refers to the measure of the directional relationship between two random variables.

How do you find the variance of a conditional probability?

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.

Is conditional variance volatility?

A key distinction is between the conditional and unconditional variance. the conditional variance is the measure of our uncertainty about a variable given a model and an information set. iii)Leverage Effects, refers to the tendency for changes in stock prices to be negatively correlated with changes in volatility.

What is conditional standard deviation?

Standard Deviation of a Conditional Distribution (Discrete Case) The conditional standard deviation of X given that Y=y is defined by: σX|Y=y=√Var(X|Y=y) While, the conditional standard deviation variance of Y given X=x is defined by: σY|X=x=√Var(Y|X=x)

How do you find covariance with two variances?

Consider two random variables X and Y. Here, we define the covariance between X and Y, written Cov(X,Y)….The covariance has the following properties:

1. Cov(X,X)=Var(X);
2. if X and Y are independent then Cov(X,Y)=0;
3. Cov(X,Y)=Cov(Y,X);
4. Cov(aX,Y)=aCov(X,Y);
5. Cov(X+c,Y)=Cov(X,Y);
6. Cov(X+Y,Z)=Cov(X,Z)+Cov(Y,Z);
7. more generally,

How to calculate the conditional variance of a centered return?

Fig. 2 shows the conditional variances of the centered returns of the series of prices under study. 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.

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).

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.

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,…