I am struggling to grasp the steps outlined in the 2009 paper by Diebold & Yilmaz, which introduces the framework for a spillover index.

The final expression for a spillover index for a two variable case is given as: \begin{equation} S = \frac{a_{0,12}^2 + a_{0,21}^2}{trace(A_0A_0')} \times 100 \end{equation}

Which are themselves components of a "One-step ahead error vector" resulting from a simple two variable vector auto regression:

\begin{equation} x_t = \Phi x_{t-1} + \epsilon_t \end{equation}

I am quite comfortable with matrix algebra and most other expressions used in the paper, however I am just completely lost in the steps outlined in the paper and frankly by what the index even truly represents.

If anyone has a slightly more intuitive formulation or description I'd greatly appreciate it.

P.S. Also if possible the creation of a spillover tag would seem appropriate.

Edit: I have also read through this paper, which has further explanations of all terms but still requires a little more ‘Terra Firma’ for me to get.


  • $\begingroup$ The first paper you link describes exactly what it is in the last paragraph on p159. The spilover index is the portion of the forecast error variance for a particular stock that is attributable to shocks on the other stocks. $\endgroup$
    – will
    Jan 27 '19 at 0:53

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