Whats the difference between applying Correlation and DTW in a Time Series I have a Financial Time Series from a database and intend to cluster the time series based on their similarity. How would it be different to cluster them based on their pairwise Correlation and cluster them using DTW. Which is recommended option between the two
 A: Dynamic Time Warping (DTW) and correlation capture very different aspects of similarity between two time-series. Which one to choose depends on what you are interested in - an information that you did not provide in your question. 
Yet I will give an example which might help to clarify the difference for you. 
Assume you consider the following two time-series as equal:
a = [1,1,2,3,4,3,2,1,1,1,1,1,1,1,1,1,1]    
b = [1,1,1,1,1,1,1,1,1,1,1,2,3,4,3,2,1]


For this example, the DTW Distance - computed as in here - returns: DTWDistance(a,b) = 0, since DTW Distance allows shift in time and effectively compares the shape of the time-series giving little importance to stretching. Whereas the correlation here returns such as np.corrcoeff(a,b) = -0.33471074 
We want to cluster objects together that are similar. Therefore we use a dissimilarity measure, which yields 0, if two objects are equal, a higher value, the more different they are. Most relevant attributes of such a dissimilarity measure would be the metric requirements such as in Wikipedia. For correlation - assuming you mean pearsons correlation coefficient - these requirements are not met. Therefore I would suggest to use DTW. Yet there might be some applications in which clustering based on correlation could yield great result. 
Best way to go: Try both and compare the results. Then choose the one which fits your expectation. 
