SEMAINE D'ÉTUDE SUR LE ROLE DE L’ANALYSE ECONOMETRIQUE ETC. 157

nents f;(#) and with residuals v, independently and normally
distributed, the TANUS quotient (75) is distributed as

m—r

(81)

Here the ¥2-variates are independent w
indicated within paranthesis: x.
squation

.u degrees of freedorr
are the roots ol

det (C. 2C,—U

where C is the product sum matrix

«

Wliüil

and C, is the corresponding product sum matrix for the prediction
 range. It will be noted from (81) that the JANUS quotient
 tends to increase with the prediction span and with the
number of free parameters.

2) Forecasting by the chain brincible

We shall consider the case of a stationary unirelation model
 M which we specify bv the representation

(82a-b)

*

5 - Br V1 +Ba V2 +
«Ly U t 1, +X, v, , =

[2] Wold - pag. 43