>> jakub.ryšánek(‘homepage’)
  Curriculum Vitae (as of 12/2012)
Some econometrics:
  Hodrick-Prescott filter
(intro + online application)
for vector autoregressions
(supplement to my Master’s
thesis, in Czech only)

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Hodrick-Prescott Filter

Technically, the efficient solution of the HP filtering problem lies in transformation of the nonlinear minimization task into a system of linear equations that represent the first order conditions of the original problem. The standard matrix algebra can then be applied.

Differentiating the criterion with respect to taut, where t takes on the values 1,...,T, results in the following system of equations:
where It is an identity matrix of order T, taut is the vector of unknown/unobserved trend components, and F is a pentadiagonal matrix with following pattern:

Unobserved trend component, taut, and the cyclical component, ct, can be derived using these formulas: