Often datasets of interest are incomplete, with the consequence that
we cannot exploit them fully in our models. Time-series data
might not cover periods of interest in sufficient detail. For
example, they might run out before a specific period of
interest. Alternatively, we might need to focus on the relationship
between two variables x and y, where beyond certain values
of x, corresponding values of y may not be known.
In such instances we are left to make estimates of
the missing data by extending what we know, as suggested
by available (measured and recorded) data.
Extrapolation means to infer or
estimate by extending or projecting known information. In mathematical terms
this involves making estimates of a value of a variable
outside a known range from values within a known range.
To do so requires us to make certain assumptions about
how the estimated values might follow logically from the known
or observed values. The following is designed to explain the
method of trend extrapolation and to indicate the
limits of its usefulness .