Questions tagged [cross-correlation]

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

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auto-correlation and cross-correlation of multivariate random processes

Assume $N$ observations of a multivariate random process $X(t)$ of dimension $q$ arranged in a matrix as it follows, where each column represents a time-series and the $i$-th row is a realization of ...
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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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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 ...
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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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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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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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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: ...
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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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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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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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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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