# Equality of Time Series

1. Jun 29, 2009

### kylemacr

Hi All,

I've searched the web up and down, and a few text books, all to no avail.

I have two time series (of 30 elements each), and I'd like to test if they are statistically different from each other (I suppose this could be reworded as, "are they equal" or "is their difference statistically different from zero"). I can't for the life of me figure out how to do that.

any ideas?

Thanks!

2. Jun 30, 2009

### g_edgar

Hire a statistician?

3. Jul 1, 2009

### EnumaElish

What kind of equality? See http://en.wikipedia.org/wiki/Random_variable#Equivalence_of_random_variables

"Equality of means" is relatively easy to test (e.g. t-test). "Equality of distributions" is harder, although I can think of the following:

1. You can study tests for equivalence of distributions, such as http://www.lesn.appstate.edu/olson/stat_directory/Statistical%20procedures/Chi_square/Chi_square_test_for_equality_of_distributions.htm [Broken] or Kolmogorov-Smirnov.

2. You can calculate the Gini coefficient then test whether it equals zero. (This may be a version of the K-S test.)

3. If you know their distributions, you can express each series as 30 successive order statistics, and jointly test their equivalence for as many orders as your degrees of freedom will let you. You'll need to derive the distribution of the difference between two order statistics, X(k) - Y(k), for k = 1 through 30, which can take some algebraic work.

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