Economists’ Untold Secrets 045: HP Filter

Economists’ Untold Secrets 045: HP Filter


Hodrick and Prescott have come up with a mechanism to decompose a data series into a growth and a cyclical component. The first equation is their intention, growth and cycle. The second their method, which is now called the HP filter. It turns out that this filter is extremely difficult to compute, and HP have used very arbitrary insertions, with respect to the parameter lamda, as well as to the variable, to make up some result. This is a result produced by someone in the internet. The problem is essentially to solve for g by minimizing the second component of this equation. But, g in the component itself is unknown. It is like trying to find a class representative without knowing the class students. HP have imitated Whittaker, but the latter used y, not g. Even if the correct variable is used, the contents of this component are second-order difference. This is a de-trend method, widely used in time-series statistics to test random walk. Not, a smoothing one for forecasting. The second component in this function is a 5-period moving average, introduced first in 1873 by De Forest. Moving average is easy to calculate. This is actually what HP themselves have used for computation. H&P have stealthily switched the bags, leaving the whole world still fumbling for the non-existing filter in the wrong bag.

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