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# How to do correlation matrix in excel

[hodrick prescott filter]

The Hodrick Prescott filter (HP filter), introduced by Hodrick and Prescott (1980), is a flexible detrending method that

is widely used in empirical macro research. Let's suppose that the original series

is composed of a trend component

and a cyclical component

The HP-Filter isolates the cycle component by following minimization problem.

The first term is a measure of the fitness of the time series while the second term is a measure of the smoothness. There is a conflict between "goodness of fit" and "smoothness". To keep track of this problem there is a "trade-off"-parameter

.Note that

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is 0, the trend component becomes equivalent to the original series while

diverges to infinity, the trend component approaches a linear trend.

As you can see the HP filter acts to remove a trend from the data by solving a least square problem. In matrix notation we get

with

.

and

It can be shown that the solution of the minimization problem is be given by

where

is the identity matrix with dimension T.

The height of the value

depends on the frequency of the data. In the literature the following values are suggested.

Source: www.web-reg.de
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