5.8 Implication 6: No High of Low Diagonals (Test for independence)

Similar to Mack’s CY Test

  • This is a test on Mack assumption 2 (prop. 4.2), no AY correlation

Key Idea: Run regression on the triangle with a dummy variable for each diagonal

Each \(q(w,d)\) is regressed against the prior cumulative losses + dummy variable for which diagonal it is in

\[\begin{equation} q(w,d) \sim c(w,d-1) + dummy_{CY} \tag{5.7} \end{equation}\]

  • If losses are significantly higher or lower in a diagonal \(\Rightarrow\) The coefficient of the dummy variable would be statistically significant (i.e. coefficient is double the \(\sigma\))

  • Only includes diagonals that forcast at least 2 elements

Caveat: Diagonal effect is additive

  • More likely to see multiplicative impact. e.g. from inflation

  • This can be implement with a regression on the logarithm of the losses

5.8.1 Diagonal Trend as Inflation

Consider CY trend as inflation and model \(q(w,d)\) with a diagonal parameter \(g(w+d)\), where \(w+d\) is the diagonal

\[\mathrm{E}[q(w,d)] = f(d)h(w)g(w+d)\]

This will have parameters for each row, column, and diagonal

  • Can be reduce similar to the grouped BF

  • We can model a constant CY trend to reduce the parameters

    e.g. \(g(w+d) = (1+j)^{w+d}\)