Questions tagged [cross-correlation]

A measure of correlation between different time series, at the same or different times.

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Cross Correlation Interpretation R

I have cross-correlation, on the left is promo and CVR checkout, and on the right is promo and CVR payment. From this figure, can I interpret that promo has high correlation to CVR payment than to CVR ...
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Given a real matrix $M$, find the closest cross-correlation matrix

Say we have an arbitrary real matrix $M$. I am wondering if we can find a cross-correlation matrix that has the least square distance to $M$. In other words, $$\min_{A,B} \|M-A^TB \|^2_F $$ s.t. $$...
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Name of this "cross-correlation type" quantity?

Suppose I have I have vectors $x_1,\ldots,x_m$ in $\mathbb{R}^d$, with $\|x_i\|=1$ for all $i$ Is there a name or statistical/geometric interpretation of the following quantity? $$\sum_{ij} \langle ...
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Multilevel cross correlation - cross correlate time series nested in participants

I have observed behavioral and questionnaire data for 45 participants over a certain span of time. Now I'd like to find out which point in time of behavioral data best predicts questionnaire data. I ...
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Kendall correlation is significant but cross correlation is not significant

I have time series data and I am confused about the output of correlation and cross correlation. This is my data: ...
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Centering in normalized cross correlation for template matching

Context I'm following Lewis (1995) exposition on normalized cross correlation for template matching (Section 2). The cross-correlation of the image and the feature at $u,v$ is denoted by $c(u,v)$ and ...
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Best way to compare two binary sequences [duplicate]

I need to compare two binary sequences and get a measure of similarity between them. Seems like the Pearson correlation coefficient is not suitable because it is for continuous signals. Is the ...
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Correlation of groups in simulating data

I am simulating time series data. Each simulation consists of a group of time series with nodes at lets say 3 levels. To get the data to adhere to the structure I only generate the terminal units (...
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What kind of statistical test might be used to if two datasets contain a non-zero lag or lead hierarchically?

I am aware of Granger causality, cross correlation, and simple methods of computing correlation at each lag/lead timestep. However, I have a dataset with 1000s of users each with a potential lag/lead ...
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Correlation within groups

I have a dataset with 200 variables. Each row of my data represents the quarter results of a company. I want to know if variable X is linearly related to variable Y. I computed the correlation matrix ...
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Finding the vectors/modes "maximally responsible" for the fluctutation of a quantity?

I have a question which I fear might be simple but i am completely unable to figure out. Lets say we have a time-series of a vector of coordinates which define a molecule ( column vector of x,y,z) ...
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Is vector-autoregression applicable to two series with Granger causality and cross-correlation that has multiple modes, both negative and positive?

Is the vector-autoregression applicable to two series with Granger causality or stationary series where the cross-correlation plot is negative at some parts and also positive in others? If that's the ...
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Comparing two cross-correlation functions with one another

Say for example I calculated two sets of cross-correlation matrices, one that compared time series A1 and A2 for 10 test subjects and another that compared time series B1 and B2 for the same 10 test ...
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Should one examine the cross-correlation plot to rule out performing Granger causality test?

Should one look at cross-correlation plot before performing Granger causality test to avoid type I errors? If we can't find any dependence between two series from the cross-correlation plot, then ...
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How does the Cross-Correlation Function of these two series suggest "bove average value of SOI is likely to lead to a below average value of..."?

library(astsa) soi= scan("soi.dat") rec = scan("recruit.dat") soi=ts (soi) rec = ts(rec) ccfvalues =ccf (soi, rec) ccfvalues Reproduce these ...
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Cross-correlation of multidimensional time-series and Python function for computing it

So far I know, the cross-correlation of two time-series $a(t)$ and $b(t)$ for which $N$ observations are available is given by $r^N(\tau)=\frac{1}{N} \sum_{t=\tau+1}^Na(t-\tau)b(t)$, where $\tau$ ...
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Temperature Lag calculation

I am working on a data science project on an industrial machine. This machine has two heating infrastructures. (fuel and electricity). It uses these two heatings at the same time, and I am trying ...
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Can you generate correlated ARMA time series with different lag orders?

Is it possible to generate correlated ARMA time series when the ARMA models are different? For example, can you generate two time series which are correlated when one is an AR(5) model and one is an ...
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Doubts with cross correlation in Python's statsmodels

I have been trying to understand statsmodels.tsa.stattools.ccf, the cross correlation between two random vectors and I tried ...
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Cross Correlation Techniques for Time Series Data [closed]

I am working with time series data and am currently using cross correlation on my data. I can use different techniques like spearman, pearson, and kendall. I was wondering if beyond that, there are ...
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Cross-correlation seems defined backwards

Suppose $f$ and $g$ are real. Why $$ C(\tau)=(f\star g)(\tau) = \int_{-\infty}^{\infty} f(t) g(t + \tau)dt \tag{1} $$ and not $$ C(\tau)=(f\star g)(\tau) = \int_{-\infty}^{\infty} f(t) g(t - \tau)dt\...
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Cross-covariance in context of Andrews plot

As shown in this Cross-Validated post Close curves on an Andrews plot I don't understand how, in the accepted answer, the cross-covariance can be defined as, $$\int_{-\pi}^{\pi}f_xf_ydt$$ Considering ...
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Spatial crosscorrelation between a binary and continuous measurement on a graph

I have a graph $G$ with vertex set $V$ and edge set $E$. I measure two signals on the vertices of the graph $X$ and $Y$. If $X$ and $Y$ are both continuous, we can measure spatial crosscorrelations ...
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Hosking test vs Granger Causality for VAR - to use or not to use?

Let's say that we have 2 stationary time series: X and Y. Granger's causality test outputs no granger causality between them, however Hosking cross-correlation test proves there is a relationship ...
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Correlation of two time series at smaller cycle

I have two multi-year time series with pronounced diel cycles. I would like to test how the diel pattern of ts1 influences the diel pattern of ts2, but I'm not clear on how to do that in R. Of course ...
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Finding correlation between two time series in R?

I am working with two time series data sets and am trying to figure out how they are related (not really interested in a predictive model though). I am not sure if Pearson correlation, cross-...
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Uncovering which frequencies two systems are communicating on by observing reoccurring time correlated signals and their frequencies

Suppose you have a set of communication systems {A, B, C, D}, which speak with each other as well as other systems not contained in the set. Our concern is how they speak with each other. They ...
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Addressing NA values when using lead relationship from the co-variate in time series forecasting using R

I'm using Arima function from the fable/fpp3 package in R for multivariate forecasting. The periodicity of the time series data is weekly and the predictor variable has 2 week strong lead co-relation ...
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PCA on two already cross-correlated time series?

I have a cross-correlation matrix of the association between two human movement time series, which have originally been cross-correlated with each other in windows and with time lags. So the matrix ...
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Filling a short time series for cross correlation

I have two times series data X and Y. X is the number of times the phrase "sole proprietorship" is searched on a local search engine while Y is the number of sole proprietorship venture ...
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How to anticipate whether a multivariate model will perform better than separate univariate models?

As the title says, I would like to know if there are any statistics or methods to check if a group of time series is multiple (i.e., independent) or multivariate (i.e., in the sense that they show ...
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Prewhitening before cross-correlation

i have a question concerning cross correlation and prewhitening of two time series. I understand the common procedure to avoid spurious correlation is to model your input series x and filter the ...
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Discrete convolution with circular matrices

Cross-correlation (read convolution) is the process of sliding a kernel across the input image and each step multiplying the elements and summing the results (i.e. matrix multiplication). PyTorch has ...
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Several significant cross correlations at various lags and with different signs? [duplicate]

I have a cross correlation plot here: I’m familiar with interpreting one obvious value at a given lag. For example, consider the positive correlation between x and y at lag -1 in the chart. This ...
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PACF-like plot but between x and y, and not y and y?

I’m interested in generating a PACF-like plot but between two separate time series x and y, with significance levels included. Just as the PACF tells us the best lagged predictors of y using lagged ...
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Don’t use first differences if you expect lagged effects?

I’m interested in seeing if two first differenced variables are cross correlated with one another (the original data are non stationary, hence I use the first differences which I show with a DF test ...
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How to optimally select window sizes for filters on spectral data

I am trying to find an efficient method of selecting a window size for a Savitzky-Golay filter. The applications is mainly to find an smooth representation of a spectra containing sharp peaks in noisy ...
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model output without correlation to input variable

let's assume that a,b,c,d,t,u,v,w,x,y,z and o are all correlated to one another. I want to make a prediction for outcome variable "o". However, I don't want my prediction to be to ...
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Expected value of product with different time indices given constant expected value of product with same time index

I am reading some notes with the following setup: $$ E[X_tY_t]=E[X_{t+1}Y_{t+1}]=\rho $$ $$ X_{t+1}=\begin{cases} X_t,& \text{with probability } \theta\\ -X_t, & \text{...
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Undertanding cross correlation between two time series

I am trying to understand cross correlation between two time series. The time series are just sine and cos of 40 numbers between 0 to 100. When I plot the cross correlation between these two time ...
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Different periodical lag in two time series and different periodical correlation interpretation

I am working on two stock price movements over 2 years, a minute by minute change (over 1m rows). I ran cross correlation after making them stationary. There is a result that I am kind of confused ...
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Detrended Cross Correlation, how sensitive is it to structural break and seasonality?

Is Detrended Cross Correlation(DCC) sensitive to structural break and seasonality? I learned that the approach is for non stationary time series, but I cannot find any information about whether its ...
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Partial Cross-Correlation, and its relationship to Granger Causality?

Definitions: Granger Causality (GC): To the future of the target channel $y(t)$ fit past values of the target channel $y(t-1)$, ... $y(t-n)$ To the future of the target channel $y(t)$ fit past values ...
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How to compute the confidence interval of a correlation function

What is the best way to compute confidence intervals of a (cross) correlation (function value at lag time $\tau$) $c(\tau)$? Typically one estimates the value $\hat{c}(\tau)$ but the question is what ...
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Interpretation of cross correlation

I need some help on the interpretation of crosscorrelation between x=credit and y=GDP, please. Here I have the results of the cc.test function in r. What I know so far, is that if the value of ...
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Understanding comment about correlation

In a paper that I'm supposed to be deep reading the author's make the statement: "We performed a cross-correlation test among the four measures composing it and found an average cross-...
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Preventing certain weights from going to 0

I would like to use a convolutional neural network to study a time series data set. I have experimental measurements taken at three different time intervals. With this I plan to create an input that ...
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Mathematical expression for a cross-correlation matrix

Given the matrices $A_{p\times q}$ and $B_{p\times q}$ with $p>q$ the cross-correlation matrix in R is calculated as: cor(A,B) The underlaying code for this is: ...
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Estimate correlation with mixed frequency data

I want to compare two mutual funds. I have fund A's weekly performance data. But for fund B, the data is less reliable. For 60% of the time, I can get hold of their weekly data, but other periods, ...
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What is the formula for the cross correlation between two random vectors?

Let $\boldsymbol{X}\in\mathbb{R}^n$ be a random vector. Then $$\text{Cov}(\boldsymbol{X}) = E\left[(\boldsymbol{X}-E[\boldsymbol{X}])^T(\boldsymbol{X}-E[\boldsymbol{X}])\right]=E[\boldsymbol{X}\...

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