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

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PDF/CDF of max-min type random variable

For i.i.d. random variables, we may write the CDF of $t=\max(t_1,\cdots,t_N)$ as $$F_t(t)=F_{t_i}(x)^n$$ and the CDF of $x=\min(x_1,\cdots,x_N)$ as $$F_x(x)=1-(1-F_{x_i}(x))^n$$ When we have $X=\...
0
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0answers
8 views

one sided hypothesis test for correlation

In the textbooks I have access to (and discuss hypothesis testing for correlation), I only met examples, where the null-hypothesis was $\rho=0$, and the alternative hypothesis was $\rho\ne 0$. My ...
0
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0answers
18 views

Average Gain, Trading Correlation

The following journal article seems to suggest Over a $5$-minute period there is a correlation between returns The average return is $0.037\%$ The average daily gain is $0.59\%$ Would anyone know ...
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1answer
23 views

Change eigenvalues of correlation matrix and transform into original basis

I use the Random Matrix Theory to filter out the information from the correlation matrix that is associated with noise - Marcenko Pastur band. That is straight forward. Then I follow Rosenow, Bernd, ...
1
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1answer
24 views

How to find an equation that describes a non-linear correlation of multiple parameters

I tried to search for this problem but I don't know what exactly I'm looking for. I found some empirical parameters that correlate but not linearly. An example follows: $Y_1$ and $Y_2$ are the values ...
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0answers
10 views

Does Averaging the score from correlation across multiple variables yield a more accurate correlation score?

This may be a beginner question but I am making a application which I using to do correlation research to be used in financial markets. The application pulls in different data sources and compares ...
0
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0answers
25 views

Hypothesis testing for the correlation coefficient

My question is related to the correlation between random variables X and Y, where $(X,Y)$ is bivariate normal. My understanding is as follows. The correlation coefficient is $\rho=\dfrac{\...
0
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0answers
32 views

Estimator for the correlation coefficient

My question is related to the correlation between random variables X and Y, where $(X,Y)$ is bivariate normal. My understanding is as follows. The correlation coefficient is $\rho=\dfrac{\...
0
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0answers
31 views

Explanation of “When two functions $a(x)$ and $b(x)$ are not correlated on domain $X$, they can be separately integrated”

Hy everyone, I was reading this paper https://hal.inria.fr/hal-00942452v1/document , and I came up with a statement that I don't fully understand, nor could I found any info on it, so decided to ask ...
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0answers
9 views

Is Markov Chain property true for correlated inputs?

I have a finite state machine (FSM). At time $k$, state is $\theta^k$ and input is $x^k$. The next state $\theta^{k+1}$ and output $y^k$ are completely determined by \begin{align} \theta^{k+1} &=...
0
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1answer
16 views

Predict value of random variable B if value of random variable A and correlation is known

Intuitively it is clear that if I have two variables $A, B \sim \mathcal{N}(\mu, \sigma)$ and I have $\rho_{A,B}=-1$, then if some sample $a$ of $A$ is $x$, then some sample $b$ of $B$ is $\mu-x$ ...
0
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0answers
22 views

Correlation matrix for linear combination of two variables and combination coefficients

I have a question: I have $N$ different linear combinations of two random variables $X,Y$ (distribution is strictly speaking unknown, but probably either normal or log-normal, and shall be the same ...
0
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0answers
7 views

What is the relationship between regression line and graph of averages?

Why is the regression line regarded as a smoothed version of the line of averages, and why is it that when the graph of averages falls on a straight line, that line is also the regression line?
1
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1answer
32 views

Why is the regression line an estimate of the average value of y for each value of x?

The regression line, passing through the point of averages with a slope equivalent to r, is said to be a good estimate of the average value of y for each value of x. I can see why this is the cases ...
1
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1answer
19 views

Best coefficient between two data sets

I want to determinate a sensor coefficient but I struggle with a basic math problem... Here are my values : ...
0
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1answer
32 views

Creating custom correlation matrix

I'd like to be able to create a matrix like the one below to be a correlation matrix. Trouble is, I cannot ensure it is positive definite, hence cannot use Cholesky factorisation, which I need to draw ...
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0answers
47 views

How can this double summation be solved?

I have to calculate the following expectation $$\mathbb{E}\left[\left(\frac1M\sum\limits_{i=1}^MX(i-n_1-M)\right)\left(\frac1M\sum\limits_{j=1}^MX(j-n_2-M)\right)\right]$$ where $M$, $n_1$ and $n_2$ ...
0
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0answers
13 views

Pearson Correlation

I have two matrices, which are square but of different size. I want to find correlation between data which is stored in these two matrices. It seems Pearson Correlation Coefficient is applicable for ...
3
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1answer
45 views

Variance of sum of linear combination

I want to calculate the variance of a sum of linear combinations, so $$\operatorname{Var}\left(w'R_1 + w'R_2\right)$$ where $w$ is a $N\times 1$ vector and both $R_1$ and $R_2$ are $N\times 1$ ...
0
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1answer
23 views

The relation of correlation coefficient of the sum of two vectors.

Does the correlation coefficient of the sum of two vectors between the correlation coefficient of each of them. Suppose I have three vectors $x_1,x_2,x_3$. The correlation coefficient of $x_1$ and $...
1
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2answers
72 views

Variance of the sum of correlated variables

If the variance of two correlated variables is: $$Var(r_1+r_2)=\sigma^2_1+\sigma^2_2+2\textrm{cov}(r_1,r_2)=\sigma^2_1+\sigma^2_2+2\rho\sigma_1\sigma_2$$ where $r_1$ and $r_2$ are vectors, then what ...
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0answers
27 views

Find the autocorrelation of $y[n]=x[2n]$ in terms of the autocorrelation of $x$

Find the autocorrelation of $y[n]=x[2n]$ in terms of the autocorrelation of $x$, given that the autocorrelation of $x$ is: $$R_{xx} = \frac 1{n\pi}\sin\left(\frac {\pi}{2}n\right).$$ I've tried to ...
0
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1answer
34 views

Given the correlation matrix, estimate the value of a random variable based on the value of other random variables. [closed]

A process generates $N$ random variables $(X_i \mid 1 \leq i \leq N)$. The process is run $K$ times, and the values of each random variable $X_i$ is observed. Based on this data, the following ...
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1answer
42 views

Can I ignore multicolinearity problem if all the regression coefficients are highly significant?

Can I ignore multicolinearity problem if all the regression coefficients are highly significant? My data is large enough and all the resulting coefficients are significant enough in less than 0.01 ...
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2answers
114 views

Is a correlation matrix with positive determinant PSD?

Please note: I'm not interested in the difference between positive definiteness and semi-definiteness for this question. A correlation matrix is a symmetric positive semi-definite matrix with 1s down ...
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0answers
13 views

statistical test for comparison of time series of rare events

I have two time series of a binary variable which assumes value 1 if an event happens and 0 otherwise. Both series report the occurrence of the same event and are not necessarily equal because the ...
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0answers
28 views

Show that $E(\mathrm{var}(Y|X)) \leq (1 - \mathrm{corr}(X,Y)^2) \mathrm{var}(Y)$

Expectation of conditional variance (Exercise 4.6.7 from Grimmett and Stirzaker): Let $X$ and $Y$ be random variables with correlation $\rho$. Show that $E(\mathrm{var}(Y|X)) \leq (1 - \rho^2) \mathrm{...
0
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1answer
49 views

How to simulate a delta-correlated random process

I'm trying to do the simulation described in the paper attached, but there is something I don't understand. The author says that the random variables which satisfy the relation (Eq. (4) in the paper) ...
0
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1answer
27 views

coefficient of determination: absence of cross products [closed]

With regard to the coefficient of determination, why is the total variation equal to the sum of the explained variation and the unexplained variation and there are no cross-products?
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1answer
31 views

What is a deviation vector?

LINEAR ALGEBRA: I've looked online for this and can't find anything... What is a deviation vector and how do I compute them? (specifically how did my teacher get those vectors in part b?) Here is ...
0
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1answer
14 views

Negative autocorrelation values

Autocorrelation is informally defined (Wikipedia article) as "the similarity between observations as a function of the time lag between them". I create the following time series in MATLAB: ...
0
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0answers
10 views

Finding a correlation between days on the market and seller rank

If you are given two variables, D = Days since a product was launched on amazon B = Bestseller Rank among a specific amazon product category How could you compare / rank a list of products based ...
1
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1answer
27 views

How to find point in polynomial regresion

I have the following data set: ...
2
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3answers
72 views

Find ratio / division between two numbers

I am reverse engineering custom software for a stepper motor. The original software eases in and out of any motion, and the duration of the ramping up to speed is directly related to the speed that ...
0
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0answers
7 views

Periodic Cross-Correlation vs Aperiodic Cross-Correlation

I am doing research in spread spectrum communication, and many papers frequently use the terms Periodic Cross-Correlation and Aperiodic Cross-Correlation. However, I cannot find a clear definition of ...
0
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0answers
14 views

$X$ and $Y$ are standardized r.v.s. Find $a,b,c,d$ such that $Z=aX+bY$ and $W=cX+dY$ are uncorrelated but still standardized.

Let $X$ and $Y$ be standardized r.v.s (i.e., marginally they each have mean $0$ and variance $1$) with correlation $\rho \in (−1, 1)$. Find $a, b, c, d$ (in terms of $\rho$) such that $Z = aX + bY$ ...
1
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1answer
37 views

Change of Uniform Continuous Variable

Let $X$ be a $U(-1, 1)$ random variable, we define $Y = X^4$. Calculate the correlation coefficient between both variables. Are they uncorrelated? PS. I don't know how to use MatJax equations, I'm ...
3
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2answers
36 views

How does the Pearson correlation coefficient change under rotations

I was reading on wikipedia about the pearson correlation coefficient. Assuming the data has zero mean it can be written as $$ \rho = \frac{ \sum x_i y_i } {\sqrt{\sum x_i^2 \sum y_i^2}} $$ The ...
0
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0answers
13 views

If all points lie on regression line, how is coefficient of correlation affected?

If all points lie on a regression line, what does that mean for the coefficient of correlation? Am I correct to say the coefficient of correlation is either -1, 0 or 1?
0
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0answers
11 views

Why does the mean centered autocorrelation have a slope of -1?

I'm fundamentally not understanding something about the autocorrelation function (as defined by numpy.correlate). Let's say I create a bunch of random signals $s_1, ...
0
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2answers
79 views

Interpretation of correlation (coefficient)

In an discussion we were confronted with a very special opinion about correlation in respect of financial assets. The widely used correlation coefficient is used here to give an idea about how ...
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0answers
13 views

First and second moments of two correlated functions

I am trying to find the first and second moments of the following: $k=mk^{-b}$ where $m \sim U[a,b]$ (discrete) and $k^{-b}$ is a power law distribution I know how to find the first and second ...
2
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0answers
52 views

How to generate correlated random numbers with specific distributions?

After read the answers of some similar questions on this site, e.g., Generate Correlated Normal Random Variables Generate correlated random numbers precisely I wonder whether such approaches can ...
2
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0answers
46 views

Formula of phase correlation

If I have two 2D signals, and one is the shift of another. I can propose such schema for define offset via continious Fourier Transform: $$f_2(x,y)=f_1(x-x_0,y-y_0)$$ Then $$Ff_2(s_1,s_2)=e^{-2\pi j(...
0
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1answer
22 views

Pearson product-moment correlation coefficient of a coin toss

A fair coin is tossed 3 times. Let $X$ be a random variable representing the number of $H$'s appeared in the first 2 tosses, $Y$ the number of $H$'s appeared in the last 2 tosses, and $Z$ the number ...
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1answer
28 views

Generating normal random variables with mean and variance [closed]

I wish to generate normals $X$, $Y$, and $Z$ with the correlation matrix $R$ but with means $0$, $1$, and $2$, as well as variances $4$, $16$, and $25$, respectively. How would you do this?
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0answers
23 views

Generaling dependent random variables

You wish to generate three standard normals $X, Y$ and $Z$ with correlation matrix given by $$R =\begin{pmatrix} 1.0 & 0.2 & 0.2 \\ 0.2 & 1.0 & 0.2 \\ 0.2 & 0.2 & 1.0 \end{...
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0answers
11 views

Normalize and Average weighted

Everyday I receive a data of three variables (neutral, negative and positive). ...
0
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2answers
30 views

Uncorrelated but not independent uniform distribution

Let $X = (X_1, X_2)$ be uniform distributed on $\{(-1,0), (1,0), (0,-1), (0,1)\}$. First of all I want to show that $X_1$ and $X_2$ are uncorrelated but not independent. Secondly I thought about ...
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2answers
36 views

Correlation Coefficient of Random Variables

Question: My work for parts a and b: Now I'm stuck with part c and don't know where to go or how to get the answer from parts a and b. any help?