Full text: Study week on the econometric approach to development planning

EWdyi—1 Viras )=Bo+B1vi_1 +85 vy, 0+... 
which is a special case of the predictive decomposition of y, 
referred to earlier in this paper [section 1.4 (4)]. The forecasts 
Yn+1> Yn+2 --- are obtained by the chain principle, making iter- 
ated use of (83). Thus when y,,; has been obtained, v,,;., 
is calculated from (83) in the basis of y,.;, v,.; 1, ... The 
variance of the resulting forecasts is given by 
E(yrumT Ans) = (1 + a? + + a? _,) ok 
showing that the accuracy of the forecast will decrease as the 
forecast span me increases. This last feature is reflected also 
in the JANUS quotient, inasmuch as (84) gives 
(85) E(J)=1+(1- 2) o24 (1-5) a+ + — ab, 
The predictive decomposition (82a-b) has the property that 
the variance (84) is the smallest possible of all representations 
of type (82b). This is the fundamental property of minimum- 
delay, established by E. RoBINsoN, Ref. 24, and referred to 
earlier in this paper. 
The approach (82)-(85) extends to the general stationarv 
case when y, allows the predictive decomposition 
Vi=Y +B ya th 
=W+v,+%, v, +a, 
where V, is the deterministic (also called singular) component 
of y,. The procedure of forecasting first settles the prediction 
of the deterministic component over the entire forecast range, 
Wold - pag. 44

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