# Hodrick-Prescott Filter

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## Hodrick-Prescott Filter

A mathematical technique used to smooth the non-linear data points in a time series. The HP filter helps analysts better determine trends. It is used most often to smooth out indices of macroeconomic data, such as the Help Wanted Index.
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The objective of the HP filter is to separate the high-frequency or cyclical fluctuations from the low-frequency or trend movements.
In particular, the measures correlated to the growth rate of GDP are all insignificant, and in the regressions against the cyclical component of GDP using the HP filter, 8 out of 18 estimates are insignificant.
Moreover, output gap is estimated with the help of five methods namely the linear trend method, quadratic trend method, HP filter, production function method, and vector autoregressive method.
As discussed by Hamilton, the HP filter produces spurious predictability in the cyclical component of a series.
Where a study uses a value for [lambda] that is too large relative to n the HP filter will yield a series that is too smooth.
However, it is only slightly above the HP filter moving average value, and it falls within the standard deviation bands of the HP filter.
(2013, 2014) analyse the real-time performance of the HP filter and show that in the US, the UK and Spain, univariate filter estimates had large upward bias before the recent crisis, which was revealed only after the crisis.
(iii) if [I.sub.i2] = [I.sub.i3] = 0 (opened), and In = Iin is given by the input current signal, a HP filter can be obtained at [I.sub.o1]
(3) Apply a 2D HP filter to the [k.sub.x]-[k.sub.y] plane for each partition of the 3D data for background suppression, where [k.sub.x] is the readout direction and [k.sub.y] is the phase encoding direction.
Pre odstranenie trendovej zlozky je pouzity HP filter [23], ktoreho vyhodou je hlavne jeho nenarocnost na vstupne data [3].
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