# Questions tagged [cross-correlation]

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

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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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### Difference between dynamic time warping, windowed cross-correlation and wavelet coherence?

I have video data with people talking with each other and I'm planning to analyse patterns of their head movements and facial expressions. I'm not very advanced in terms of statistics, so could you ...
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### Cross correlation of a time series with volatile variance

I have two time series datasets representing 2 variables(x and y)which I want to cross correlate. I'm using autoarima() in R to define the time series structure of x, but the acf plots of the ...
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### Extract the Knowledge From Time Series Dataset

I have a time series sensor data that contains lots of sensor readings from equipments and some categorical values about equipments (On/Off/Ready, etc). I have observed that one of my sensor value got ...
25 views

### 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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### Taylor diagram on two timeseries data

I am wanting to explore the relationship (correlation) between measured data and predicted data of temperature at monthly intervals. Both sets of data are timeseries, where observation 1 of the ...
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### Statistical test for time-series lag identified via cross-correlation?

The cross-correlation (https://en.wikipedia.org/wiki/Cross-correlation) is often used to identify the presence of constant time offset between two time-series. In short, two time-series are correlated ...
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### Using a Dynamic Linear Model

I'm working on a time series project where part of it involves the analysis of two time series. When looking at the CCF plot under the call ccf(data1, data2), I note the following: A higher cross-...
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### Interpret the correlation structure and infer causation

I have a dependent variable $y$ and search for possible exogenous variables $x_i$ for $i = 1, ..., n$. One possible way is the correlation structure. I know the difference between correlation and ...
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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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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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### Do I need to have the same number of data points in both time-series for cross correlation?

For example, I have rainfall data for 30 days. But I have flood extent data for only 7 days. So do I need to create a third time series comprising of the same days for which I have flood extent data? ...
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### Is it possible to cross-correlate rainfall data and flood extent?

(I am very new to statistics and in my first year of undergrad. So I am extremely sorry if my questions sound dumb but please bear with me). Basically I want to find out whether upstream rainfall ...
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### Difference between plt.xcorr() at (1+)-lag and np.corrcoef()

I use plt.xcorr() function to plot cross-correlation between time series: ...
16 views

### 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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### Testing species association and clustering : Multivariate analyses / weighted association test

Sorry to take a bit of your time but I am slightly (very) lost, and very unsure as to which test to use in R. Alright so here is the oversimplified sampling procedure, with easy-looking numbers : -We ...
22 views

### 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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### Cross-correlation two time series in R

I’m processing data on daily web visits in R for two pages (on the same domain) for 2020. I want to know if the trends (daily increases/decreases) in visitors follow a similar pattern on both pages. ...
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### Does a time series clustering that uses cross-correlation as proximity measure require stationarity?

I have a set of time series which exhibits no autocorrelation but the variance is not constant. I remember that one of the requirements of cross-correlation to be meaningful is weak stationarity (we ...
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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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### What is the best approach to modelling local time series house prices?

I have a dataset of house prices over time and have broken it down into neighbourhoods. For each neighbourhood I would like to create a time series model that captures the local price movements. What ...
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### How to test whether extreme price deviations are correlated?

I have a panel data set of the minute-by-minute OHLC (i.e. Open, High, Low, Close) prices of Bitcoin from multiple exchanges. I would like to test whether the extreme price deviations (i.e. the ...
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### How do I model 2 variables that both affect eachother?

I am trying to model the relationship between tourism traffic and the proportion of coral reef bleached over time. I noticed that an increase in tourism will increase the proportion of reef bleached ...
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### Map between variables, using cross-correlation

I have a cross-correlation matrix, $C_{nm}$, between two sets of variables, and I would like to establish the correspondence between the row and the column variables. My current approach is to convert ...
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### Cross correlation of time series in a cluster

I have 15000 time series each of length 288 (corresponding to a sample taken every 5 minutes during a single day), and I want to group these time series by how similar they are based on shape and y-...
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### Why does the residual and variable cross correlation function tell us about cross independence?

I am new to time series. I understand that the sample autocorrelation function (SACF), if Xt is white noise, then for large (n), the SACF is approximately normally distributed with zero mean and ...
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### Finding relationship between two variables?

Suppose I have 3 big baskets of apples (basket A, B, C), each of the 3 big baskets are separated into smaller baskets according to the apples' weights. *Apple's weight varies. The weights are going up ...
26 views

### Filtering time series based on arima coefficients for prewhitening

I've been following this tutorial for pre-whitening time series in order to apply CCF. In the example, the authors use an ARIMA(1,1,0) model, which is then defined as presenting the following ...
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### Cross-Correlation and Outliers

I'm currently cross-correlating two time series and a visual inspection of the bivariate joint distribution indicates an outlier. I am using Pearson correlation, so I know that I should remove it to ...
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### Identifying lead/lags using multivariate regression analysis

I have three time-series variables (x,y,z) measured in 3 replicates. x and z are the independent variables. y is the dependent variable. t is the time variable. All the three variables follow diel ...
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### Cross Correlation for grouped Time Series

I have two time series datasets that take place over a period of 7 years for a few thousand areas (7 data points for each area). Which would look like: ...
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### What is the relationship betwen covariance, covariance matrix and cross-correlation?

I am not good at math and apologize if I made stupid mistakes in this question. Assume I have two random variables X = [1, 2, 7, 3, 0, 10 ...] and Y = [12, 1, 5, 7, 9, ...]. According to the ...
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### Testing for transformation-errors in different signals

Let's suppose I have two signals, or time series (for this matter). The first time series (let's call it "A"), is a collection of measurements made every 15 minutes. Time Value 08h00 2.6 ...
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### How to ascertain positive correlation between random variables?

Suppose we have random variables~$X,Y,Z$ that are related by the following: \begin{equation} X = Y + f(Z) \end{equation} for some function $f$. Under what conditions on the random variables and $f$ ...
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### Determine confidence interval in a 2D cross correlation map

My problem is as follows: I have a 2D image (u,v), with each pixel representing the value of the 2D cross correlation function (ccf) at that place. I am trying to determine to what degree I can be ...
23 views

### Normalised Cross-correlation VS sliding Pearson coefficient

Let's imagine we have two signals, x and y, and their normalised cross-correlation M. Would the entries in matrix M correspond to a sliding Pearson coefficient, i.e. we take signal x, and we shift the ...
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### If time reverses the Wide Sense Stationary(WSS) preserves or not?

If $X(t)$ is WSS with autocorrelation $R_{X}(\tau)$ then is $Y(t)=X(-t)$ WSS? How to find Cross Correaltion of $X(t)$ and $Y(t)$ too? And, can we say they are jointly WSS?
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### Is RMSE a good non-parametric substitute for Pearson's r?

I am examining how well two non-stationary time series, which are supposed to be representing the same thing, match each other. I believe I should, therefore, be specifically looking for a linear ...
285 views

### Interpretation of cross correlation plot in Python

I am working on stock prediction problem. I want to see how two closing values are related. Steps performed so far: Normalized the close value for both stocks so that I have data on similar scale. ...
38 views

### How to check/compute correlation between historical data?

How can I find out if there exists a correlation between this two specific time series of historical data Market Price (https://www.blockchain.com/charts/market-price) and Difficulty (https://www....
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### Anomaly detection for multiple correlated variables (sensors)

I have time series data from multiple sensors detecting vehicles driving through the sensor zone. I'm aggregating the total actuations for each sensor in 15-minute bins. The sensors are correlated, ...
16 views

### How to mitigate the effect of Cross-Correlation between Explanatory and Dependent variables

I have explanatory and dependent quaterly time series variables. Seasonality was removed from both variables. This is cross-correlogram between those two variables generated by Stata. I have tried to ...
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### Fisher's formalism : How to find a complementary matrix to respect the Maximum Likelihood Estimator (MLE)?

I make following a previous post : Bad attempt to do cross-correlations between 2 matrices Indeed, I say "Bad attempt" since the beginning of this study, I did a major error. By wanting to ...
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### Cross-correlation - fewer data points at the edge?

I have a question about cross-correlations that I can't seem to get my head around. From my understanding, when I perform a cross-correlation between two time-series, one time-series will be shifted ...
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### How to quantify a prior or information into a Fisher matrix?

I have 2 Fisher matrices of the same dimension, each one representing parameters that I have to constain by combining these 2 matrices in Fisher's formlism. Firstly, I did a simple sum between both to ...
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### Modelling of two time series data which seem to move together?

I have two time series data, these two data when looked at graphically seem to move roughly together i.e. on a higher level the shape of the two is similar. I want to apply some kind of modeling to ...