I have a simple time series with 5-10 data points per data set at regular intervals. I am wondering what is the best way to determine whether two data sets are different. Should i try t-tests on each data point, or look at the area under the curves or is there some kind of multivariate model that would work better?

**Answer**

You will need to specify precisely what you mean by “different”. You will also need to specify what assumptions you are willing to make about the serial correlation structure within each time series.

With t-tests, you are comparing the *mean* of each group and you are assuming that the groups consist of independent observations with equal variances (the latter is sometimes relaxed). When testing time series, the assumption of independence is usually not reasonable, but then you need to replace it with a specified correlation structure — e.g., you might assume that the time series follow AR(1) processes with equal autocorrelation. Consequently, even comparing the means of two or more time series is considerably more difficult than with independent data.

I would carefully specify what assumptions I was willing to make about each time series, and what I was wishing to compare, and then use a parametric bootstrap (based on the assumed model) to carry out the test.

**Attribution***Source : Link , Question Author : Dave , Answer Author : Rob Hyndman*