Correlation of Distances

#1
I am trying to measure geometrical similarities of given two time-course data. Each of two time course data measures independently something changing over time. Suppose counting how many ice-creams are sold every day in August and measuring temperature every day. Both the number of ice-creams and temperature are a function of time. Are the time-course function changes in similar or different fashion? I have tried: (a) Peason's correlation of correlation; (b) Correlation of Distances; and (c) Cross correlation. Do you think which is the most appropriate method? I need to calculate the similarity in a quantitative manner with considering data continuity.
 
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