The polynomial distributed lag model is based on the assumption that a distributed lag model:
shows polynomial dependency between βj and the number j, that can be expressed as:
Using this assumption, the equation can be rewritten as:
Introduce the notations:
Then the model looks as:
Model parameters can be estimated using the standard OLS method.
To apply the Almon's method, first define the number of lags q. This number is commonly found by selecting a reasonable maximum and gradually reducing this number. After defining q, the user should find the degree of polynomial r. The following rule is commonly applied: polynomial degree must exceed the number of extremum points at least by one (extremum points are the points that separate intervals of function increase and decrease) depending on βi = β(t - i). However, as the degree of polynomial grows, the probability of having unaccounted multicollinearity also increases due to specifics of defining the variables z. This increases standard errors of the coefficients γj.
See also:
Library of Methods and Models | Distributed Lag Models