Recently, I came across this algorithm called "Dynamic Time Warp" (e.g. https://cran.r-project.org/web/packages/dtw/vignettes/dtw.pdf).
Although this algorithm looks quite involved and complicated, it seems that the main purpose is to determine if two (seemingly different - e.g. two people walking at different speeds) time series are "similar to each other". It also seems that the DTW algorithm can be used for clustering time series data as well (https://cran.r-project.org/web/packages/dtwclust/vignettes/dtwclust.pdf).
Has anyone ever used the DTW algorithm before? What kind of problem did you use it on? What industry did the data come from (e.g. environmental, finance, etc.)? Was it successful? How exactly did it help you in your work/research?
Does it make sense to use the DTW algorithm to check if two stock returns (or financial time series) are related to each other? I am confused as to why this algorithm is useful. Once you have found out that two time series are "related", what can you do with this information? Does DTW answer similar questions as Granger Causality or Cointegration?