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 ...
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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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10
votes
Accepted
Interpreting output from cross correlation function in R
To answer your question, here is an example:
...
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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-...
- 118k
7
votes
Accepted
"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 ...
- 7,048
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 ...
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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 ...
- 50.8k
6
votes
Accepted
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 ...
- 64.9k
6
votes
Accepted
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.
...
- 1,605
6
votes
Accepted
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 ...
- 31.9k
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 ...
- 532
5
votes
Accepted
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 ...
- 518
5
votes
Accepted
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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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).
...
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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 ...
- 29.1k
4
votes
Accepted
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
Accepted
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_{...
- 20.2k
4
votes
Accepted
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 ...
- 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 ...
- 211
3
votes
Accepted
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 ...
- 64.9k
3
votes
Accepted
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 ...
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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 ...
- 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 ...
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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....
- 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-...
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3
votes
Accepted
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 ...
- 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 ...
- 1,605
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. ...
- 4,011
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 ...
- 29.1k
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