Prequential Model

We are interested whether a sequence of forecasts ⚠ $f_1,f_2,\ldots$ agrees with a sequence of outcomes ⚠ $x_1,x_2,\ldots$. The prequential model corresponding to this sequence of forecasts is the forecasting system ⚠ $\phi$ that outputs the forecasts ⚠ $f_1,f_2,\ldots$ regardless of the outcomes. If our criterion of agreement respects the strong prequential principle, ⚠ $f_1,f_2,\ldots$ agrees with ⚠ $x_1,x_2,\ldots$ if and only if ⚠ $\phi$ agrees with ⚠ $x_1,x_2,\ldots$.

Bibliography

• A. P. Dawid. Fisherian inference in likelihood and prequential frames of reference (with discussion). Journal of the Royal Statistical Society B 53:79 - 109, 1991. Section 7.3.