Development of the Spatial Credibility Model - Cont

  • Inserting this into equation 2 gives:

    Cov(Xt0, Xjv) = ?i,u aiu Cov(Xiu, Xjv) = ?i,u aiu [?uvg(i,j) + f(i,j)]

    or:

    Cov(Xt0, Xjv) = ?i aiv g(i,j) + ?i,u aiu f(i,j)

  • Notice that the left hand side of this equation can also be evaluated as:

    Cov(Xt0, Xjv) = ?0vg(t,j) + f(t,j) = f(t,j)

  • This produces the following simplification of equation 2:

    (4) f(t,j) = ?i aiv g(i,j) + ?i,u aiu f(i,j)

    for all values of year v.

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