13 votes

What does it mean for a time series to be autocorrelated?

Take the time series without the first observation, $X_2, \dots, X_T$, and the time series without the last observation, $X_1, \dots, X_{T-1}$. You have two vectors of length $T-1$. Calculate their ...
Stephan Kolassa's user avatar
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(...
Ami Tavory's user avatar
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10 votes
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Interpreting output from cross correlation function in R

To answer your question, here is an example: ...
Jon's user avatar
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9 votes

What does it mean for a time series to be autocorrelated?

"Auto-correlation" is correlation "with the self" at different points in time The prefix "auto" means self or same (from the Greek "autós") so "auto-...
Ben's user avatar
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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 ...
Ruben van Bergen's user avatar
7 votes

Measuring level of uncorrelation from correlation matrix?

Perhaps the tolerance statistic is something that could be helpful for you. It is defined as 1 - R^2 for a given variable, where R^2 is calculated based on a linear regression of that variable on all ...
Christian Geiser's user avatar
7 votes
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Measuring level of uncorrelation from correlation matrix?

It turns out that if you take the inverse of the correlation matrix, then take the reciprocal of the diagonal elements of the inverse, the result is one minus the $R^2$ values from the regression ...
Greg Snow's user avatar
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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 ...
Richard Hardy's user avatar
6 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. ...
Michael Grogan's user avatar
6 votes
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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 ...
user20160's user avatar
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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. ...
MaxBenChrist's user avatar
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 ...
Rob's user avatar
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5 votes
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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 ...
Miguel M.'s user avatar
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5 votes
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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. ...
Fato39's user avatar
  • 824
4 votes

Interpreting output from cross correlation function in R

I checked the ccf function with a small example from Box and Jenkins (1976, p 374-375). ...
Claude's user avatar
  • 126
4 votes

Find correlation between two time series. Theory and practice (R)

Your very straightforward simple question has unfortunately both a simple and a complex answer. I will avoid the simple . In summary the whole idea is that one needs to account for / condition for ...
IrishStat's user avatar
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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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Testing significance of correlation between time series

Bartlett's theorem is useful for this. If $\{\mathbf{X}_{t}\}$ is a bivariate time series whose components are defined by $$ X_{t1} = \sum_{k=-\infty}^{\infty} \alpha_k Z_{t-k,1}, \hspace{10mm} \{Z_{...
Taylor's user avatar
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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 ...
user20160's user avatar
  • 31.9k
4 votes

What does it mean for a time series to be autocorrelated?

Autocorrelation as a function: is that function random, deterministic? It's from the point of view of the autocorrelation function and its nature that one could shed some light on the idea of ...
calocedrus's user avatar
3 votes
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Pearson correlation coefficient for lagged time series

But when the two variables are arranged in a certain lag and then Pearson correlation coefficient is calculated between them, can we still say that the variance explained will be equal to the square ...
Richard Hardy's user avatar
3 votes
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How to test if I can use cross-correlation?

The sample cross correlation function is useful to identify which variable is leading or lagging. You can learn more about it here. Note that if you have non-stationary data you may find some spurious ...
Regis A. Ely's user avatar
3 votes

Normalized correlation with a constant vector

Let $\boldsymbol{x}$ and $\boldsymbol{y}$ be your two vectors and let $\boldsymbol{\bar{x}} \equiv \bar{x} \boldsymbol{1}$ and $\boldsymbol{\bar{y}} \equiv \bar{y} \boldsymbol{1}$ be constant vectors ...
Ben's user avatar
  • 118k
3 votes

Statistical test for cross-correlation

For auto-correlation, one can use the Box-Cox or variations (e.g. Ljung–Box) to test if any number of auto-correlations are jointly significant. The basis of these tests is that some weighted sum of ...
Kruggles's user avatar
3 votes

Partial Cross-correlation in R

Look at my answer to my own question (same as the one you posted). You can make use of the pacf function in R, extending it to a matrix with 2 or more time series....
Miguel M.'s user avatar
  • 518
3 votes
Accepted

Finding correlations between financial time series

Find correlation between two time series. Theory and practice (R) discusses my road-map which is quite consistent with the very clear presentation that you cited http://svds.com/avoiding-common-...
IrishStat's user avatar
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3 votes
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Is there any relationship between Granger causality and Cross-correlation diagram?

I just spoke to a great econometrician he informed me the following: In Granger test, we factor out the auto-correlation coefficients, and hence we only focus our attention on the cross-correlation ...
Anonymous's user avatar
  • 353
3 votes

Finding Correlation between Time Series - is it a meaningless value?

Traditional correlation measurements between two time series will not tell you much. As an example, let's take the issue of height across both cross-sectional and time series data. Cross-sectional ...
Michael Grogan's user avatar
3 votes
Accepted

correlation of predictions and actuals

Toy example: Z X Y 1 3 100 2 2 200 3 1 300 $cor(X,Z) = -1, cor(Y,Z) = 1$ while $SSE_{xz}<SSE_{yz}$ I'd say it's a matter of scale. ...
Łukasz Deryło's user avatar
3 votes

Cross-correlation of two non-stationary time series?

why don't you post your data and I will try and help you. Box and Jenkins suggested pre-filtering where the differencing operator identified as part of the ARIMA process was used as part of the filter ...
IrishStat's user avatar
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