Hodrick-Prescott filter for trend and cyclical components

`hpfilter(S)`

hpfilter(S,smoothing)

T = hpfilter(...)

[T,C] = hpfilter(...)

`hpfilter(S)`

uses a Hodrick-Prescott filter and a default smoothing parameter of 1600 to separate the columns of`S`

into trend and cyclical components.`S`

is an*m*-by-*n*matrix with*m*samples from*n*time series. A plot displays each time series together with its trend (the time series with the cyclic component removed).`hpfilter(S,smoothing)`

applies the smoothing parameter`smoothing`

to the columns of`S`

. If`smoothing`

is a scalar,`hpfilter`

applies it to all columns. If`S`

has*n*columns and`smoothing`

is a conformable vector (*n*-by-1 or 1-by-*n*),`hpfilter`

applies the vector components of`smoothing`

to the corresponding columns of`S`

.If the smoothing parameter is

`0`

, no smoothing takes place. As the smoothing parameter increases in value, the smoothed series becomes more linear. A smoothing parameter of`Inf`

produces a linear trend component.Appropriate values of the smoothing parameter depend upon the periodicity of the data. The following reference suggests the following values:

Yearly — 100

Quarterly — 1600

Monthly — 14400

`T = hpfilter(...)`

returns the trend components of the columns of`S`

in`T`

, without plotting.`[T,C] = hpfilter(...)`

returns the cyclical components of the columns of`S`

in`C`

, without plotting.

[1] Hodrick, Robert J, and Edward C. Prescott.
"Postwar U.S. Business Cycles: An Empirical Investigation." *Journal
of Money, Credit, and Banking*. Vol. 29, No. 1, February
1997, pp. 1–16.

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