Hodrick–Prescott filter

The Hodrick -Prescott filter is a mathematical means of macroeconomics to analyze business cycles. It is used to compensate for a time series, so that it is less dependent on short-term fluctuations. The Hodrick -Prescott filter separates the trend of a time series of the cyclical component. With it, you can see the time series stationarisieren.

The formula

It is the logarithm of the time series. If positive, there is a trend component, which minimizes the following expression

The first term is the sum of the squared deviations. The second term is a multiple of the sum of the squared difference of the trend of the second component. This term penalizes the variation in the trend component. The higher, the greater the punishment. Robert J. Hodrick and Edward C. Prescott use of quarterly figures. The Hodrick -Prescott filter is a two-sided filter. It can compensate for the trend flexible than a simple linear filter.

The filter was indeed named after Hodrick and Prescott, but probably has the mathematician John von Neumann earlier invented a similar means.

The HP filter is admittedly the most popular means for eliminating a cyclical component, yet he is often criticized. In particular, the filters at the edges to a distortion as to be used for the edge estimate values ​​to differences can form. In addition, the filter by construction can not identify a longer trend deviations. He is, by the choice of, set to a certain maximum length of the economic cycle. A recession of more than three years would already be counted as a downward trend. ultimately remains a freely - chosen variable that has no theoretical foundation.

Modification

To solve the problem of distortion at the edges, used to Switzerland, which is dependent in the context of the debt brake on this filtering process, a modified version, the modified Hodrick -Prescott filter as above. The weights of the last period are reduced, so that the distortion is neutralized.