Questions tagged [cross-correlation]

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

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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 ...
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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 ...
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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 ...
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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. ...
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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, ...
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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 ...
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What is the essence of Linear Discriminant Analysis while considering the correlated features for Inter Class problem?

Suppose, I have samples from APPLE, MANGO, and ORANGE --- these 3 classes. The goal is to do multiclass classification. Now, let's say, I have calculated 4 features from all of the 3 classes. By rules ...
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Coherence using FFT: how to calculate coherence for one frame

I want to calculate coherence between two time series that are of equal lengths. Since coherence is given by Pxy/(sqrt(Pxx)*sqrt(Pyy)) , I did the following steps. Step 1: Divide both time series (...
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Cross-correlation synthesis for 2 Fisher matrices

I am trying to do a synthesis between 2 Fisher matrices, i.e without only considering a simple sum : I am looking for a final Fisher matrix that performs the XC (cross-correlations). One done that, I ...
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Cross correlation lags

At what lag, relative to a time series length, does the cross-correlation stop being applicable? Say for two time series of 100 data points each I examine the lag 99 correlation. I'm only comparing ...
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how to get total Fisher matrix that makes cross synthesis of 2 Fisher matrix

I have initially posted on physics.stackexchange but I think my issue is more adapted on Cross-Validated (so I am going to delete the initial post on physics.stackexchange). I have 2 Fisher matrixes ...
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Cross correlation between sequences of events

If I have a Poisson-like process generating events at times $T=\{t_0, t_1, ..., t_n\}$, and two different derived sub-sequences $X$ and $Y$ such that: For all $x\in X$ then $x\in T$. For all $y\in Y$ ...
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Interpretation of CCF plot

I am using ccf on two univariate time series to find out which variable is leading and which is lagging. My result is something like shown in the plot Can I really tell anything from this plot? Does ...
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59 views

Methodology of cross-correlation of two time series

I have two time series. They are the same length of 3 years and each with one variable. I want to know if the two time series are correlated at a certain time point - 1 month, 2 month, 3 months etc. ...
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Estimate the delay between two signals

I have two voltage time series from two sides of a battery with 20 seconds resolution. The signals are non-periodic and voltage2 is usually half the ...
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Selecting study design ( and tests) to precise the optimal interval of checkups of engine to prevent engine major failures

I'd like to get your advice on how to select methodology and plan database variables (skeleton ) to conduct a retrospective research. there are around 60 engines, they can have major failure (main ...
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Prediction model of test scores based on subjective assessment

I am trying to build a model where I want to measure the accuracy with which supervisors can predict the outcome of test taker's scores. For example, supervisors rate test taker's subjectively before ...
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Time Series Multivariate Forecasting

I am building a time series forecasting model in which I am considering the macroeconomic indicators as predictors.I wanted to understand 3 things How do I generally go about feature selection for my ...
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No apparent relation between two time series data

I have two time series data and I want to understand relationship between them for my a data science project that I am currently working on. The time series plots are given below : The plot of 1-...
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Time delay detection in time series

I'm trying to align series of weather data. I have two temperature and pressure sensor which in some time periods has been shifted by some time. Example data with offset equal to -600min I need to ...
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How to correctly pre-whiten time series

I'm trying to find cross -correlation between two-time series and as it so happens, they are auto-correlated(2), nonstationary and co-integrated. As I read about them, it appears that pre-whitening ...
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Correct process to find cross correlation between two time series step by step

I have two time series dataset, of which I have two variables Error_Count and Bookings_made for a duration of 33 months. I wish to find if and how strong/weak is the correlation between these two ...
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Time-series with non-synchronous trends. Any recommendation?

Could you please help me with good approaches for non-synchronous time-series events? I have the following scenarios: Time series data with number of events in a month (For instance: Medical events ...
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Summing Differently-Distributed, Correlated Random Variables

I have four mutually correlated time series. Each contains 40 observations but is fundamentally and decisively differently distributed from its peers. The first series follows a Laplace distribution, ...
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Is there a way to evaluate the performance of cross correlation model in R?

I am trying to test the effect on the heat flux between indoors and outdoors before and after removing insulation. ...
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Multivariate time series vs panel data vs?

Apologies for the clunky question, I'm just looking for recommendations for the type of model I should be looking into. I can do the research from there, I just don't even know what to look up at the ...
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Panel unit root tests - How to determine the lag order?

I am using Pesaran's panel unit root test in the presence of cross-sectional dependence. How do I specify the lag order? I find that the results of my tests changes when I change the number of lags. ...
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Find Correlation between Grouped and Ungrouped Data

I have 2 datasets. First is a Quarter-yearly data that has PTR (Pay-through-rate) value associated with an Agent for every Quarter. The second dataset has the detailed data for Sales related to those ...
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How do you interpret results from crossCorrelation in R from spatialEco package?

I want to use the crossCorrelation function from the R package https://rdrr.io/cran/spatialEco/man/crossCorrelation.html spatialEco to examine the relationship between people's perceptions and the ...

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