Abstract
Two special classes of covariance matrices are considered which give simplified computations for linear forecasts without continued reinversion of the matrix. In the first class, the optimal coefficients in the forecast can be computed in advance for every time period by simple closed formulae. In the second class, which includes the first, the optimal coefficients are obtained through a simple first-order linear recursive relation between forecasts of successive time periods. Collective risk forecasting models which give rise to covariances of these types are presented.

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