Correlation, linear or curvilinear

In summary, there are different methods for measuring correlation depending on the type of relationship between variables. The Spearman's rank correlation coefficient is used for non-linear relationships and does not depend on underlying distributions. However, it requires data to be ordered from small to large. When dealing with time series data, the autocorrelation function is commonly used, which measures the influence of past variables on current variables. It can give a measure of any type of correlation, but multiple lags must be considered to get a clear understanding of the relationship. The method also assumes a normal distribution.
  • #1
fisico30
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correlation, linear or curvilinear...

Hello Forum,

usually the Pearson coefficient is meaninful to find the linear relationship between two variables. What if the relationship is not linear? How about quadratic? I heard of the Spearman’s rank correlation coefficient, which does not depend upon the assumptions of various underlying distributions. This means that Spearman’s rank correlation coefficient is distribution free. This method seems so first need the data to be ordered from small to large.

However, I am dealing with time series. Data, I guess cannot really be ordered, since we want to compare values a specific instants of time.
In textbooks, I usually find autocorrelation function as a function of lag tau. It is computed as the integral of the product of f(t) and f(t+tau), all divide by T->very large, where T is the interval of observation.
What type of correlation does this method give? Does it measure a linear correlation or any type of correlation?
Why does it take only the product between f(t) and f(t) at another time instant, instead of f(t1), f(t2) and f(t3), i.e. at three instant of time? Or at four instants...?
I think there is some Gaussianity assumption on the time series going on here...but I still can't understand the reason for just two time instants...
I am dealing with time series. In textbooks, I usually find the autocorrelation as a function of lag tau. It is computed as the integral of the product of f(t) and f(t+tau), all divide by T->very large, where T is the interval of observation.
What type of correlation does this method give? Does it measure a linear correlation or any type of correlation?
Why does it take only the product between f(t) and f(t) at another time instant, instead of f(t1), f(t2) and f(t3), i.e. at three instant of time? Or at four instants...?
I think there is some Gaussianity assumption on the time series going on here...but I still can't understand the reason for just two time instants...

thanks
fisico30
 
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  • #2


fisico30 said:
Hello Forum,

usually the Pearson coefficient is meaninful to find the linear relationship between two variables. What if the relationship is not linear? How about quadratic? I heard of the Spearman’s rank correlation coefficient, which does not depend upon the assumptions of various underlying distributions. This means that Spearman’s rank correlation coefficient is distribution free. This method seems so first need the data to be ordered from small to large.

However, I am dealing with time series. Data, I guess cannot really be ordered, since we want to compare values a specific instants of time.
In textbooks, I usually find autocorrelation function as a function of lag tau. It is computed as the integral of the product of f(t) and f(t+tau), all divide by T->very large, where T is the interval of observation.
What type of correlation does this method give? Does it measure a linear correlation or any type of correlation?
Why does it take only the product between f(t) and f(t) at another time instant, instead of f(t1), f(t2) and f(t3), i.e. at three instant of time? Or at four instants...?
I think there is some Gaussianity assumption on the time series going on here...but I still can't understand the reason for just two time instants...
I am dealing with time series. In textbooks, I usually find the autocorrelation as a function of lag tau. It is computed as the integral of the product of f(t) and f(t+tau), all divide by T->very large, where T is the interval of observation.
What type of correlation does this method give? Does it measure a linear correlation or any type of correlation?
Why does it take only the product between f(t) and f(t) at another time instant, instead of f(t1), f(t2) and f(t3), i.e. at three instant of time? Or at four instants...?
I think there is some Gaussianity assumption on the time series going on here...but I still can't understand the reason for just two time instants...

thanks
fisico30

Your questions are a little vague but as far as time series analysis goes one tries to estimate the influence of past variables on current variables. If the sampling distributions are normally distributed then the auto-correlation function measures the influence of the past variables on the present. However a single lag will not give you a clear answer. You must simultaneously measure all of the lags to get independent estimates of their individual influence.
 

FAQ: Correlation, linear or curvilinear

What is correlation?

Correlation is a statistical measure that describes the relationship between two variables. It indicates whether and how strongly the variables are related to each other.

What is the difference between linear and curvilinear correlation?

Linear correlation is a type of correlation where the relationship between two variables can be described by a straight line. Curvilinear correlation, on the other hand, is a type of correlation where the relationship between two variables cannot be described by a straight line, but rather by a curved line.

How is correlation calculated?

Correlation is calculated using a formula called the correlation coefficient, which measures the degree of linear relationship between two variables. The value of the correlation coefficient ranges from -1 to +1, with 0 indicating no correlation, +1 indicating a perfect positive correlation, and -1 indicating a perfect negative correlation.

What does a positive correlation mean?

A positive correlation means that as one variable increases, the other variable also tends to increase. This indicates a direct relationship between the two variables.

What does a negative correlation mean?

A negative correlation means that as one variable increases, the other variable tends to decrease. This indicates an inverse relationship between the two variables.

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