I have two time series; (1) with average daily temperature (which is negative in Q1 and Q4 on some days) and (2) gas consumption of a client:
A part of the process I am trying to achieve is to calculate the relationship between gas consumption and temperature. I expect the consumption to be higher on average when it's colder. How shall I calculate the correlation between the two series?
I can check the correlation between the absolute values of temp in deg.C and gas consumption, the correlation between the log (temp,t-1 / temp,t) & log(consumpt,t-1 / consumpt,t), or either of the options with the temperature in Kelvin. Every method gives a substantially different result and I do not know which is correct. Any input would be helpful.