Estimation of the term structure by linear regression
Suppose that the discount function can be expressed as the linear combination of the 
functions that are twice continuously differentiable functions as
where
We can estimate the weights 
by generalized least squares. We will discuss the choice of the functions 
later. The estimated discount function is the function of the estimated weights 
.
Let D denote an 
matrix whose elements 
are 
, and 
be the vector that contains the weights . Thus 
and
which is a linear regression model under the constraint that 
, which can be expressed as follows:
where 
.
The GLS estimation for the weights of equation (2) under the constraint of equation (3) is
where
