# Questions tagged [conditional-variance]

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### Loss function for conditional variance?

Minimizing square loss results in predicting conditional means. Minimizing absolute loss results in predicting conditional medians. What loss function results in predicting conditional variances? I ...
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1 vote
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### Conditional distributions of correlated normal random variables

Suppose that $X$ and $Y$ are normally distributed with mean zero and nonzero covariance. I want to know the distributions of $X | X - Y > c$ and $Y | X - Y > c$, which I believe should be ...
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### What is the intuition of a GARCH model without fitting ARMA for the conditional mean?

I wanted to ask, as I've seen this used a couple of times before, about the logic of fitting a GARCH model in absence of estimating ARMA for a series that is clearly an ARMA process (Fitting a GARCH ...
1 vote
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### Modelling the Conditional Variance in a Panel Setting

I am familiar with ARCH-type models to estimate the conditional volatility of some variable of interest in a univariate setting. I know that there also exists the concept of multivariate ARCH-type ...
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### How to model conditional variance?

Sorry if this question has been asked before; I'd love to read any discussion around this. There's got to be a better way to summarize this question as well. I've got covariates $X$ and response $Y$, ...
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### Conditional bias-variance decomposition of MSE

The MSE can be decomposed as follows: \begin{align*} \mathbb{E}\left[(\hat{\theta} - \theta)^2\right] &= \mathbb{E}\left[\left(\hat{\theta} - \mathbb{E}(\hat{\theta}) + \mathbb{E}(\hat{\theta}) - \...
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### What is conditional normal variance of $X$ given that dependent $Y$ is bigger than a real number $M$? [duplicate]

There are two dependent normal variables with the same distribution and the correlation coefficient $\rho$: $X,Y \sim N(\mu, \sigma^2)$. I would like to get $P(X>M|Y>M)$. For that I need to know ...
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### Does endogeneity imply heteroskedasticity?

Consider two random variables $X,Y$, with supports $\mathcal{X}$ and $\mathcal{Y}$, respectively, finite for simplicity. Assume that the map $$x\in \mathcal{X} \mapsto E(Y|X=x)\in \mathbb{R}$$ is ...
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1 vote
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### Var(e|X), when e=Xu (from Hansen's Econometrics book)

I was working through Bruce Hansen's Econometrics book/notes and got tripped up over something that should be very simple. See the snapshot below, which comes from page 25 of his book Econometrics. ...
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### How to show that an m.d.s is not independent?

I have to prove that this Martingale Difference: $x_t = u_t u_{t-1}$ where $u_t \sim^{iid} (0, \sigma^2)$ is not serially independent, but am failing to do such thing. I also have to prove that it's ...
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