In econometrics, Prais–Winsten estimation is a procedure meant to take care of the serial correlation of type AR(1) in a linear model. Conceived by Sigbert Prais and Christopher Winsten in 1954, it is a modification of Cochrane–Orcutt estimation in the sense that it does not lose the first observation, which leads to more efficiency as a result and makes it a special case of feasible generalized least squares.
Contents
Theory
Consider the model
where
for t=2,3,...,T, Prais-Winsten procedure makes a reasonable transformation for t=1 in the following form
Then the usual least squares estimation is done.
Estimation procedure
To do the estimation in a compact way it is directive to look at the auto-covariance function of the error term considered in the model above:
Now is easy to see that the variance–covariance matrix,
Now having
where
Note
To see why the initial observation assumption stated by Prais–Winsten (1954) is reasonable, considering the mechanics of generalized least square estimation procedure sketched above is helpful. The inverse of
A pre-multiplication of model in a matrix notation with this matrix gives the transformed model of Prais–Winsten.
Restrictions
The error term is still restricted to be of an AR(1) type. If