>> 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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The HP filter is a very popular filtration technique in the field of time series analysis.

In the usual decomposition of a time series one can identify the trend component, the cyclical component, and the seasonal component (apart from random disturbances). The HP filter usually takes seasonally adjusted time series as an input and decomposes it into the two remaining components - trend and cyclicality.

Though, in its essence the HP filtering technique leads to a nonlinear optimization, first order conditions of the problem collapse into a system of linear equations that can be solved using simple matrix algebra.

Since the 1980s when the HP filter was first applied in economics (in other fields had been known even before), the algorithm has become a standard tool for extraction of the business cycle information contained in the data - namely separation of the potential output and the output gap.

In comparison to other techniques, such as the production function approach or the Kalman filter, the HP filter forms a fast and easy to use alternative.