e are interested in forecasting of quantity
based on information
.
The information comes as a flow. So, at first, we know
.
Based on
we compute the projection
.
Then we receive additional data
and obtain
.
Our goal here is to express
as a function of
,
and
.
Such result would provide a recursive relationship useful for general
situation of long information flow
.
Our
computation below is motivated by the fact that for
we
have
In general
and
are not orthogonal so we make a
correction:
