As I looked the discussion in above mentioned question link, I think it is more towards the correlation between two dependent variables with respect to time. Since you want to ignore time while calculating the correlation, if all the dependent variables are present for a given time stamp vector, they can be directly used in regression. For example.
If time is from t = 1 sec to 100 sec with interval of 1 sec and price and demand is available for each of those time value then price and demand can directly be used as two pair of vectors for calculating correlation.
Also, if the correlation between time and price, time and demand is meaningless, it is better to do regression between price and demand since it will show the correct trend.