# compare the means of two cross sectional time series

I have bi-variate annual ($$n=6$$) time series data for each company $$i$$ (number of companies $$k=5$$): $$\begin{bmatrix} X_{it} \\ Y_{it} \end{bmatrix} ,\, i = 1,\dots, k,\, t = 1,\dots, n$$ Where $$X_{it}$$ and $$Y_{it}$$ are not independent ($$X$$ is actual profit and $$Y$$ is expected profit).

We want to test if there is a significant difference between $$X$$ and $$Y$$ with this data? What is the appropriate test?

I think it may use t-test or Wilcoxon test for each company and get $$k$$ decisions (one for each company), but I don't know how can we damage all this results together.

I thought also that if we combined the data of all companies together, it might be possible to compare common means (actual and expected).

• Difference between $X_{t}$ and $Y_{t}$ when? For example, if $X_{t} = Y_{t}$ except at a single point in time, would that be "difference" for you? How large would such a difference need to be? What is the specific question you want answered? (There is no "general" difference, only specifics, see my answer here.) – Alexis Feb 28 at 17:13
• many thanks @Alexis. It is helpful. – Kourabi Mar 5 at 7:22