I have several temporal signals of different dimensions, for example the motion of a point throughout time which would be of dimension 3, and the value of a temperature sensor, of dimension 1.


I would like to find out if these signals are correlated. Is there a measure of correlation that works for signals that do not have the same dimensionality?



Correlation measure between signals of different dimensions?
Yes, you can use multiple regression, with temperature as the dependent variable and the three space dimensions as the independent variables. 


