I have a time series with prices (around 800 prices). I need to test if the mean is constant during all the series.

I think I should subdivide the series in groups, but what method do I have to use to check if the mean is constant if the distribution is *not* normal?

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#### Best Answer

You may want to look at a nonparametric approach to this problem, since you cannot rely on normality. Break your sample into two groups, $x_1, dots, x_{400}$ and $x_{401}, dots, x_{800}$ and compare them in pairs ($x_1, x_{401}$), $dots$, ($x_{400}, x_{800}$).

You now have the framework of a two-sample test of equal means/medians. Under the null hypothesis of a constant mean, we should expect the mean/median of these two groups to be the same.

Since we expect the medians to be the same, some NP tests will assert that in the pair $(x_i, x_{i+400})$, the chance that $x_i$ is bigger is a random variable, Bernoulli distributed with probability $frac{1}{2}$. Two hypothesis tests proceed from this. Tests to look into would be: Wilcoxon Signed Rank Test and the Signed Test.

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