Would the cosine measure be the appropriate similarity measure to use with K-means clustering for time series data? Why or why not? If not, what similarity measure would be more appropriate?

What will be an ideal response?

Time series data is dense high-dimensional data, and thus, the cosine measure
would not be appropriate since the cosine measure is appropriate for sparse
data. If the magnitude of a time series is important, then Euclidean distance
would be appropriate. If only the shapes of the time series are important,
then correlation would be appropriate. Note that if the comparison of the
time series needs to take in account that one time series might lead or lag
another or only be related to another during specific time periods, then more
sophisticated approaches to modeling time series similarity must be used.