# covariance's questions - English 1answer

1.016 covariance questions.

### Calculating the covariance between 1-D arrays for incorporation into propagation of uncertainty

I have four 1-D arrays of dependent variables. They contain hundreds of data points but I have cropped them to 20 in this example. Each point represents a grid cell on a map. ...

### 1 How do I find the “elliptical confidence region” from columns of a matrix that follows the Wishart distribution?

The subject is about the sample mean and the sample covariance estimators and their respective confidence regions for the estimated parameters. Suppose that $n$ samples are taken from a $p$-variate ...

### 3 Requesting Intuitive Explanation to Covariance, Correlation and Standard Deviation

First I would like to state that I am not from a mathematical background. I am studying about change in price of products. So I have to understand about Correlation , Covariance and Standard Deviation ...

### 2 Covariance of random variable with product of random variables

I have the following covariance term: $Cov(x,yz)$ with $x$, $y$, and $z$ being random variables with a mean and variance. I found a paper by Bohrnstedt and Goldberger from 1969, On The Exact ...

### 1 Covariance versus correlation: which is a “deeper” or more “structural” property of the data?

It might seem obvious that the covariance is a "deeper" property of the data generation process (DGP), since normally the specification of a joint distribution is done in terms of its mean vector and ...

### 1 how to do decorrelation and covariance equalisation?

In order to improve the convergence of a MLP, one should do "mean removal", "decorrelation" and "covariance equalization". I know how to do mean removal, but how do you do decorrelation and ...

### 1 What happens with Mahalanobis-Distance, when the assumption of equal Covariance-Matrices breaks down

Assume that we want to compare the forecast quality of various forecasters $f$ on $n$ values such as stock-market prices or whatever. We could then define a "Mahalanobis-Distance" (MD) (or rather ...

### Covariates and moderator variables

1 answers, 19 views interaction covariance ancova
I have a 4 * 3 (both the IVs are categorical) factorial design with two covariates (both are continuous) to run ANCOVA. Can I do a moderation analysis?

### 1 covariance matrix vs correlation matrix for multiple signal analysis

I'm dealing with a set of +100 input signals, and one output. I want to explore how each of the signals affects the output. Should I focus on covariance matrix, or correlation matrix, and why? I ...

### 12 Covariance of a random vector after a linear transformation

2 answers, 4.068 views mathematical-statistics covariance
If $\mathbf {Z}$ is random vector and $A$ is a fixed matrix, could someone explain why $$\mathrm{cov}[A \mathbf {Z}]= A \mathrm{cov}[\mathbf {Z}]A^\top.$$

### 18 How does the formula for generating correlated random variables work?

3 answers, 1.789 views correlation normal-distribution covariance
If we have 2 normal, uncorrelated random variables $X_1, X_2$ then we can create 2 correlated random variables with the formula $Y=\rho X_1+ \sqrt{1-\rho^2} X_2$ and then $Y$ will have a correlation ...

### 6 What's the value of $\text{cov}(x, x^TAx)$, when $x$ follows a normal distribution

When $x\sim N_k(\mu,\Sigma)$ is a multivariate normal distribution, $A$ is a symmetric matrix, how can I show that $$\text{cov}(x, x^TAx) = 2\Sigma A\mu$$

### 1 Is there any correlation between forecasting errors from forecasting done at different origins?

Let $\ e_{T+l|T} = Z_{T+l} - \hat{Z}_{T}(l)$ be the forecasting error $\ l$-steps ahead when the forecasting origin is time $\ T$. Now, let $\ e_{T+l-j|T} = Z_{T+l-j} - \hat{Z}_{T-j}(l)$ be the ...

### 5 Prove that $\text{Corr}(X^2,Y^2)=\rho^2$ where $X,Y$ are jointly $N(0,1)$ variables with correlation $\rho$

Consider jointly distributed random variables $X,Y\sim N(0,1)$ that have $\text{Corr}(X,Y)=\rho$. Show that $\text{Corr}(X^2,Y^2)=\rho^2$. (Hint: Consider $X,U\sim N(0,1)$ where they are ...

### 2 AR(1) - autocorrelation calculation

1 answers, 21 views self-study covariance autoregressive
I am practicing deriving proofs and I cant seem to yield the correct answer for the covariance of an AR(1) model: $$X_t=pX_{t−1}+e_t.$$ Would greatly appreciate if someone could tell me where I am ...