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).

  • $\begingroup$ 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.) $\endgroup$ – Alexis Feb 28 at 17:13
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    $\begingroup$ many thanks @Alexis. It is helpful. $\endgroup$ – Kourabi Mar 5 at 7:22

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