# Comparing the means of two time series

I have data sets of the returns of two indexes in the same market (two different sets of stocks constituting each index), with 496 observations for each. I want to compare if the means are statistically different. I believe the variances are different, so I think I have to check if the variances are statistically different first. How would I do these things?

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This question didn't completely make sense to me. Please make sure it still asks what you want to know. Further, can you provide more detail about your data & what you want to know from it & thus, what you want to know from us? Are you wondering how to do a t-test?, if t-tests are valid if the variances differ?, how to adapt a t-test if the variances differ? something else? –  gung Jul 31 '12 at 2:02
Do you need to know how to run a t-test in your software? (What software are you using?) Are you wondering what a t-test is / how it works? –  gung Jul 31 '12 at 3:14
If two data sets of returns with different variances and different means, is it valid to use t-test, and if yes? how? I'm using excel –  James Jul 31 '12 at 3:18
My data is 496 observations of two sets of returns, the sets represents two indexes, I got the descriptive statistics, and both have different means and variances, I want to compare the difference between the means, is it statistically significant ?? or I would check the Sharpe Ratio difference is is statistically significant ? the bottomline I want to check if the outperformance of is statistically significant –  James Jul 31 '12 at 3:41

The t test is primarily employed for data that is paired ( e.g. N independent pairs of readings before and after some activity) or for N independent readings on two characteristics (indices). You don't have independent observations since you have time series data that is most probably auto-correlated (within structure). The cross-correlation coefficient (among structure) also requires independent (within structure) draws as there is a requirement for joint normality which requires statistical independence of the draws. Again time series data is by it's very nature not usually independent. Please see "Why Do We Sometimes Get Nonsense Correlations between Time-series?" (1926), an investigation of a form of spurious correlation, in http://en.wikipedia.org/wiki/Udny_Yule AND http://empslocal.ex.ac.uk/people/staff/dbs202/cat/stats/corr.html for more. The best way to determine the relationship between two time series is to review How to identify transfer functions in a time series regression forecasting model?.

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