11 votes

Why is the correlation coefficient a limited measure of dependence?

This is explained in the Wikipedia entry for Correlation and Dependence. Correlation basically measures how close two variables are to having a linear relationship between them. Consider now $X \sim U(...
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9 votes
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Interpreting output from cross correlation function in R

To answer your question, here is an example: ...
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8 votes

Interpreting CCF correlation in R

Your interpretation of the plot is correct. The only significant cross-correlation at the $5\%$ level of significance is at lag zero. Thus, we cannot say that one variable leads the other variable (...
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8 votes
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Is my time series stationary?

Tests for stationarity are notorious for having weak power so keep that in mind. As mentioned in the comments, it helps to use judgement as well. A weakly stationary process by definition has a ...
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  • 535
7 votes
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How do you generate correlated ARMA(1,1) models?

I know that you want the correlation between the series themselves but a valid way (and to me the most natural way) to achieve it is by choosing the correlation between the disturbance terms. As I ...
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7 votes
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"Associative" Correlation

None of them are (generally) true, and this is easy to prove by counterexamples. If $E[XY]\ne0$,$E[YZ]\ne0$ then can we say $$E[XZ]\ne0$$ Suppose we have: $$X=A+B$$ $$Y=A+C$$ $$Z=C+D$$ where ...
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6 votes
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Cross correlation for very sparse binary data

You are right to think of correlation as the mean of the product of the standardized variables: this has great conceptual advantages over other definitions. It also leads to minimal loss of floating ...
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6 votes
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How to perform proper data mining on time-series data?

I'll take the alternative approach to @forecaster and suggest you have the option of not treating this as a time series problem. Instead, with A as the response, ...
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6 votes
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Cross-correlation between two seasonal series

The essential question is, what problem are you trying to solve? If you intend to build a good model for the data (and later use the model for hypothesis testing, forecasting or whatever), you need ...
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5 votes

Cross-correlation significance in R

The cross-correlation coefficient does not measure dependence between time series. The proper tool for it is the coherence function. For example, see Bendat and Piersol, 2010.
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  • 51
5 votes
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Random variables have non-zero covariance but expected sample covariance is zero? (intuition)

The conditions on the covariances will force the $X_i$ to be strongly correlated to one another, and the $Y_j$ to be strongly correlated to each other, when the mutual correlations between the $X_i$ ...
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5 votes

Feature selection for time series data

I was also on the search for a list of time series features quite a while ago. There are publications inspecting individual features but I was not able to find a comprehensive list of features. ...
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5 votes

How can I make the correct time-series analysis for my data?

You would likely be looking to calculate the residual autocorrelation function (RACF), also called residual cross-correlation function, which is the autocorrelation function on the residuals of fitted ...
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Does the partial version of the Cross Correlation Function exist? If so, how can it be computed?

So, after some research on the topic... I came to realise that if you execute the following code: pacf(ts(cbind(dx,dy)),lag.max=10) You get the partial cross ...
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Why are the results of R's ccf and SciPy's correlate different?

The difference is due to different definitions of cross-correlation and autocorrelation in different domains. See Wikipedia's article on autocorrelation for more information, but here is the gist. ...
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How to analyze correlation of multivariate time series

What you're calculating (the correlation between $A$ and lagged copies of $B$ and $C$) is called the the cross correlation. This isn't typically suitable for testing causality because it neglects the ...
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4 votes

Asynchronous (irregular) Time Series Analysis

I know of one possible solution, but it is sufficiently complicated that I'm going to take the easy option and link you to the relevant academic paper (a critically under-rated paper in my opinion): ...
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4 votes
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Finding a subset of the data in which two variables are independent

I guess some procedure of blind search could be designed in order to test correlations in various partitions of your sample. Assume that you indeed find a sub-sample in which what you think must hold, ...
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4 votes
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Multivariant time series in R. How to find lagged correlation and build model for forecasting

You need to use your ACF & PACF behaviours to help you determine which model suits your data better (e.g. an existence of slow decay in ACF plot indicates that differencing might be needed to make ...
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4 votes

Convert Cross Correlation to Probability value

Cross correlation measures the similarity of two signals / images A,B Only in a very particular sense. Two things can be highly correlated but very different in size (mean, say) and scale (variation ...
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4 votes
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Interpreting CCF correlation in R

How can I extract only acf value for lag=0? The acf at lag 0 ($\text{corr}(X_t,X_t)$) is always 1. Do interpret it correctly that there is a cross-correlation for the lag=0, as for this lag the ...
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4 votes

Reproduce Cross Correlation results in Python

Just as a note, here is the Python solution based on @whuber code: ...
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Spatial Cross-correlation Function

The estimator you are referring to comes from Bias and Variance of Angular Correlation Functions. $D$ is an empirical sample of galaxies, typically captured as a CCD image. $R$ is a simulated ...
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Code for detrended cross-correlation in R

Alright, I finally find my mistake. It is before the final line of the DCCA_CC function. instead of rho = F2_dcca / (F2_dfa_x * F2_dfa_y) It must be ...
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4 votes
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What type of analysis to choose for this data?

You clearly have a bimodal (multimodal for the second) distribution: standby (on the left) cooling (on the right) It does not seem that the temperature settings affects the power intake. Most ...
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4 votes
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Reference to equation of correlation of log-normal random variables

You can find it in Johnson and Kotz (1972) p20. [1] an alternative reference (that refers to Johnson & Kotz) is Lai, Rayner & Hutchinson (1999) [2] [1] Johnson, N. L. and Kotz, S. (1972). ...
4 votes
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What is the difference between Cross Correlation and Correlation Matrix

When it comes to correlation, there are several types in the realm of time series analysis. Cross correlation is only one measure - which is referring to the correlation of one signal with another. ...
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4 votes
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Interpretation of logistic regression with normalized features

The interpretation of logistic regression coefficients is similar in the case where you've standardized the data (subtract mean, divide by standard deviation of each feature). By standardizing, you ...
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3 votes
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Reproduce Cross Correlation results in Python

Background The referenced paper is about evaluating the strength of chess players. The data consist of computer evaluations of the strengths of individual moves (for one game in this example but, in ...
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3 votes

How to perform proper data mining on time-series data?

Have a look at the ARIMAX model specification. It seems to be closest to what you're doing. You can use any nonparametric regression or classification model given concatenated Toeplitz design ...
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