For questions about correlation of two random variables. Use it with [tag: random-variables] and [tag: probability].

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Modelling Correlation between CAC and DAX index

I am working on the implementation of a Garch-copula model ("Patton" approach who did it on exchange rate) to model the correlation between these two index. It is implemented now. Basically, you first ...
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2answers
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Let $X = -10Y + 10$. Let $r_1$ be the correlation between $X$ and $Z$ and $r_2$ be the correlation between $Y$ and $Z$.

Let $X = -10Y + 10$. Let $r_1$ be the correlation between $X$ and $Z$ and $r_2$ be the correlation between $Y$ and $Z$. Then, which of the following is the best answer? $r_1 = r_2$. $r_1 = 10r_2$ ...
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2answers
45 views

Covariance/Correlation Proof

I'm having a little problem with a statistics problem I am working on. I'm not really sure where to start to prove the two statements. Any help would be greatly appreciated. Let $x$ and $y$ be ...
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1answer
44 views

The mathematics of Correlation is not equal to Causation

In statistics, it is a common practice to say that "correlation does not mean causation", and mostly the proof for this is given by examples. While that is good for the intuition, it's not rigorous. ...
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16 views

Proof that space of correlation matrices is compact

An $n\times n$ real symmetric matrix is a correlation matrix, if it is positive-semidefinite and all its diagonal entries equal 1. According to most references it is easy to see that the space of ...
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16 views

Combined Effect size

Is there a way to calculate the effect size between more than 2 components? For example, if i know the effect size of variable A on C and I also know the effect size of variable B on C, is there a ...
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1answer
25 views

How can I solve $\phi_1$ and $\phi_2$?

Let be $$\rho(1)=\frac{\phi_1}{1-\phi_2}, \rho(2)=\frac{\phi_1^2+\phi_2(1-\phi_1)}{1-\phi_2}$$ How can I solve $\phi_1,\phi_2$? My idea: $\rho(1)=\frac{\phi_1}{1-\phi_2}\Leftrightarrow ...
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17 views

Relationship/correlation between data - does it exist?

Data I refer to in this question Some analysis has been conducted for my business by an external company. The data, as it stands, only really tells part of the story and doesn't provide any real ...
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1answer
23 views

Can I get $\mathrm{Cov}(X_1, X_2)$ in this case?

I know the values of: $\mathrm{Cov}(X_1,Z_1)=M_1$, $\mathrm{Cov}(X_1,Z_2)=M_1*A$, $\mathrm{Cov}(X_2,Z_1)=M_2*B$, $\mathrm{Cov}(X_2,Z_2)=M_2$ Is it possible to get the value of ...
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8 views

Bounded Stochastic discrete process

I just came across this stochastic process (link): $dY_t = (a-bY_t)dt + c \sqrt{Y_t(1-Y_t)}dW_t$, where $dW_t$ is a Wiener Process. According to the author under certain conditions this process is ...
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Problems about Farlie-Morgenstern family of bivariate CDFs

Hi I am trying to solve the following problem: Let $F_X:\mathbb{R}\to[0,1]$ and $F_Y:\mathbb{R}\to[0,1]$ be unnivariate Cumulative Distribution Functions (CDFs) and suppose $-1\le\alpha\le 1$. Define ...
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1answer
28 views

Correlation of three values

I have a data set that considers three values, $x,y,z$. And I have three questions: What's the relationship between $x$ and $y$? What's the relationship between $z$ and $y$? What's the relationship ...
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1answer
22 views

Why is autocorrelation used without normalization in signal processing field?

According to the wikipedia(Link), autocorrelation has two definition. Oh my god! In statistics, the definition of the autocorrelation between times $s$ and $t$ is like the following: $$\displaystyle ...
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0answers
16 views

What do you call Binomial Distributions Correlated like this?

If we have two biased coins, and throw both $n$ times, then we can describe the probability of getting $a$ heads with the first coin and $b$ heads with the second coin, as a product distribution of ...
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1answer
31 views

Orthogonality of Two Signals.

My last question's link: Reconciling different definitions of orthogonality However, I failed to understand why they are equivalent. If $f$ and $g$ are real, \begin{align} ...
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22 views

How to calculate the correlation between two ratings

Suppose x and z are two persons who rate a classical piece of music y on a five point scale. x rates y $3$ out of $5$ z also rates y $3$ out of $5$ I need to know how much the ratings of x ...
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1answer
46 views

Reconciling different definitions of orthogonality

I want to establish about orthogonality in my mind. I knew the orthogonality of two functions $f$ and $g$ in interval T like the following: $$ \int_{<T>}f(t)g^*(t)~dt=0 \tag{1} $$ where $$ ...
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10 views

Correlate normal shocks

I am trying to generate some random standard normal variables and correlate them In particular I want: $$ \bf Y \sim \mathcal N(0, \Sigma) $$ where $\textbf{Y} = (Y_1,\dots,Y_n)$ is the vector I ...
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0answers
38 views

Correlation between $X$ and $Y$ where $X$,$Y$ are from i.i.d. standard normals and $X+Y > 0$?

Suppose $Z = X + Y$, where $X$ and $Y$ are independent standard normal random variables. If we generate plenty of $(X,Y)$ pairs and only keep the ones where $Z>0$, what's the correlation between ...
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1answer
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What is the correlation between the pairwise differences of 2 bivariate normal random variables? [closed]

Given (X,Y) bivariate normal, $U = \frac{X_i - X_j}{\sqrt2\sigma_x}$ and similarly $V = \frac{Y_i - Y_j}{\sqrt2\sigma_y}$ for any two independent pairs $(X_i, Y_i)$ and $(X_j, Y_j)$. Why is this true ...
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1answer
21 views

Sum of two standard variables with joint bivariate distribution?

Let $X_1$ and $X_2$ have standard normal distribution and let $(X_1,X_2)$ have a joint bivariate distribution. Can anyone explain why: $X_1+X_2=\sqrt{2+2\rho}Z$ where $Z\sim N(0,1)$ and $\rho$ is the ...
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0answers
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Correlated Normal Random Variables with Circulant Matrix [migrated]

Let $\Sigma \in \mathbb{R}^{n \times n}$ be a circulant, symmetric, positiv definite matrix. To generate correlated random variables $Y$ with the covariance matrix $\Sigma$, one has: $$ Y = C X $$ ...
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2answers
27 views

Is there any difference between Correlation and Correlation coefficient?

I learnt in probability theorem class that correlation coefficient is $$ \rho=\frac{\sigma_{XY}}{\sigma_X \sigma_Y}=\frac{E\left[(X-\mu_X)(Y-\mu_Y)\right]}{\sigma_X \sigma_Y} $$ However, my ...
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2answers
29 views

How does Variance become an Autocorrelation Function?

"For a Gaussian stochastic process $X=\{X(t)|-\infty<t<\infty\}$ with mean function $\mu(t)=0$ for all $t$, its autocorrelation function is $$ E(X(t)\cdot X(s))=R(h)=\max(0,1-|h|), h=t-s. $$ ...
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1answer
33 views

Relation between correlation and regression

Let $y\in \mathbb{R}$ be a random variable. Let $y$ be expressed as a linear combination of $x_i$ $i=1,2,\cdots,n$, as follows \begin{equation} y = \sum\limits_{i=1}^nw_ix_i + \epsilon \end{equation} ...
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111 views

Can't find the relationship between two columns of numbers. Please Help [closed]

I cannot find the relationship between these two columns...other than I know that they both increase or decrease in value at the same time. I'm not a math person, but I would appreciate any help ...
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0answers
31 views

Autocorrelation function of a Wiener process & Poisson process.

Can anyone possibly explain step 3 and 4 in this solution?
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3answers
70 views

Correlation between $(X+Y)^2$ and $X$

Good evening everybody! I am totally puzzled about how to solve this problem. We are given the random variables $X$ and $Y$, both of which are independent and uniformly distributed on $[0,1]$. Then ...
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2answers
36 views

Autocorrelation function of integral of cont. white noise

Let $W(t)$ be continuous time white noise, that is, a wide-sense stationary (WSS) zero-mean Gaussian process with autocorrelation function $R_W (\tau) = σ^2\delta(\tau)$. Calculate the auto ...
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1answer
22 views

Need Help explaining this equation for the correlation coefficient

As I am not a math geek so I have problem comprehending this equation: equation for the correlation coefficient Its basically the formula used in the CORREL functon in Microsoft Excel and I am ...
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0answers
33 views

Why is the length of a BAPS (binary almost perfect sequence) a multiple of 4?

a BAPS is a binary sequence of length $n$ with an almost perfect autocorrelation: $$ A(\tau)=\left\{\begin{matrix} n & \tau=0 \\ k & \tau= {n \over 2} \\ 0 & else \end{matrix}\right. $$ ...
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8 views

Distance correlation

How good is distance correlation by Gabor Szekely(https://en.wikipedia.org/wiki/Distance_correlation) to detect correlation between categorical and continuous random vectors?
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Measuring correlation of two time series

I have two sets of annual time series (employment growth from 2 different sources), which I display by using index. I would like to measure somehow whether series 1 (which are more timely) can be used ...
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78 views

Minimum and maximum bound on mean of product of three pairwise uncorrelated random variables

There are three pairwise uncorrelated random variables $X, Y, Z$ $$E(X) = E(Y) = E(Z) = 0$$ $$E(X^2) = E(Y^2) = E(Z^2) = \sigma^2$$ How we could find minimum and maximum bound on $E(XYZ)$? I ...
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Show covariance matrix must have condition number larger than correlation matrix

The inverse of covariance matrix can be used to find the conditional independencies among variables. This inverse is more sensitive to changes then the correlation matrix. As a result two samples with ...
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General correlation between function with itself and other input data

I've collected data for a function F = f(g(x)), for different function shapes g(x). The goal is to predict values of ...
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1answer
22 views

Correlation Coefficient

I am trying to understand the following equation for Correlation Coefficient: $r = \frac{\sum_{i=1}^{n}(x_i-\bar x)(y_i-\bar y)}{\sqrt(\sum_{i=1}^{n}(x_i - \bar x)^2\sum_{i=1}^{n}(y_i-y)^2)}$ ...
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1answer
19 views

calculate mean of two variables given two regression equations

Given these 2 regression equations how do I compute mean and find $r_{XY}$. $X=-0.4Y+6.4$ $Y=-0.6X+4.6$ when I rearranged the equations, I solved for $X$ and $Y$ hence $X=6$, $Y=1$ How do I get ...
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Minimal conditions to show $\sum \rho_{ij} \Psi_{ij} s_i s_j < \sum s_i s_j $

Consider a sequence of real number $\{s_i\}_{i\leq n}$. Now consider the real numbers $F$, $G$ and $\alpha$ defined below $$F= \sqrt{ \left( \sum ~\rho_{ij} ~\Psi_{ij}~ s_i ~s_j \right)^+}, $$ $$G = ...
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1answer
38 views

Constructing a sample by correlation

Suppose we have two samples with known correlation (should be relatively high). Say both samples have $n$ data points. What if now we still know the correlation factor but one sample only consistent ...
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1answer
18 views

wss process and autocorrelation

In a paper, I saw a quiz question about auto-correlation of a WSS process than I can not understand. It says: Let $X(t)$ be WSS. Which of the following can be correct? a) $E[X(t_1) X(t_2)] = |t_1 - ...
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63 views

Uniform Random Variable: Correlation and Independence

Let X be a uniform random variable defined on the interval $(0,1)$. If $Y = 6X^2−6X+1$, compute the correlation of X and Y . Are X and Y independent? Are X and Y uncorrelated? So my work is. $F(X) ...
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1answer
69 views

Positive definiteness of a correlation matrix

With $n$ natural numbers 1, 2, ..., $n$, there are $N=n(n-1)/2$ unique pairs that are the 2-D indices for random variables $z_{ij}$ ($1 \le i < j \le n$). I have the correlation matrix $A$ of ...
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9 views

Mean value given error is distributed ~ N( 0 , .1 )

The true weight of an object is w It is weighed two different times X1 and X2. Then X1 = w + E1 and X2 = w + E2 Where E are the two measurement errors. Suppose the error is iid with a mean of 0 ...
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24 views

Gaussian Copula Function

I have a question that I believe I know the answer to, but I would like to double check. Is it possible to use a copula function to calculate the joint probability of three or more variables? I'm ...
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19 views

Correlation coefficient of a block matrix

My question is related to the computation of correlation coefficient of a block covariance matrix. The correlation coefficient can be computed as: r = $ cov(X,Y)/std(X) std(Y) $ But if I have a ...
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30 views

Probability of at least one event ocurring given correlations

I have a problem that I can't solve. I have three variables. Let's call them $A$, $B$, and $C$, and the specific probabilities of them ocurring, $\text{P}(A)$, $\text{P}(B)$, $\text{P}(C)$. I also ...
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How to derive distribution of correlation coefficients under bivariate normal condition

X and Y are bivariate normal and r is the correlation coefficients. If X,Y independent. I want to show : $\frac{r}{\sqrt{(1-r^2)/(n-2)}}$ follows $t_{n-2}$ distribution.
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17 views

Proof about the ranks of a correlation matrix

$C$ is the correlation-matrix of the random variables $B_1,B_2,\dots,B_n$. These random values are the columns of matrix A. I calculate the elements of $C$ using this formula: Where I have to ...
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33 views

How to Discover Function Relating Two Variables

I have two variables, call them $x$ and $y$, that can possess any arbitrary positive integer value. I have an automated process that produces an output based on these variables. I do not, however, ...