Correlation, linear or curvilinear

[fisico30]

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

 

[wofsy]

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.