The model implies that the innovation in price is δtPt observable. Since (3) can be written pt = (dt + Etpt+I), we know, solving, that Etpt+1p =t/-dt. Hence StPtj Etpt -Et- Pt = pt + dt- Il- Pt- Y Apt +dt-1-rpt-1. The variable which we call
St Pt (or just δp) is the variable which Clive Granger and Paul Samuelson emphasized should, in contrast to Pt= Pt-Pt-1p, by efficient markets, be unforecastable. In practice, with our data, δtPt so measured will approximately equal pt.