I have two data sets of pollutant concentration on simultaneous days. I have to check whether these two curves follow similar pattern or not ( there might be some time lag between both) on daily basis. The variation in my curve is not regular and straight inspite shows peak variation at some time and low concentration at other times. I have to examine the existence of consistence based on each day.
How can I explain it mathematically and prove the variation to be statistically significant ?
Could someone suggest /help Thanks Gracy
https://en.wikipedia.org/wiki/Cross-correlation is what you are looking for.
If you had data points for 2 curves, you'd normalize them (make their sum equal 1) and perform "cross correlation" which is basically convolution without flipping anything.
The maximum value (out of 1) will tell you how similar the two curves are and the position of the peak will tell you how much delay there is between them.