Skip to contents

X-11 Selection of Trend-Cycle Filter

Source: R/icr.R
x11_trend_selection.Rd

Performs X-11 selection for the length of the Henderson filter (x11_trend_selection()) and computes the associated I/C ratio used to build Musgrave filters (find_icr()).

Usage

x11_trend_selection(x)

find_icr(length, freq = 12)

Arguments

x

A "ts" object representing the time series.

length

Integer specifying the length of the filter.

freq

Integer specifying the frequency of the time series used to compute the I/C ratio (e.g., 12 for monthly, 4 for quarterly).

Value

  • x11_trend_selection() returns a named numeric vector containing the selected length and the associated I/C ratio.

  • find_icr() returns a single numeric value corresponding to the I/C ratio associated with the specified filter length and frequency in the X-11 algorithm.

Details

The following procedure is used in X-11 to select the length of the trend filter:

  1. Computes the I/C ratio, \(icr\), with a Henderson filter of length equal to the series frequency plus 1.

  2. The selected length depends on the value of \(icr\):

    • If \(icr < 1\), the selected length is 9 for monthly data and 5 otherwise.

    • If \(1 \le icr < 3.5\), the selected length is \(freq + 1\) (i.e., 13 for monthly data, 5 for quarterly data).

    • If \(icr \ge 3.5\), the selected length is 23 for monthly data and 7 otherwise.

  3. The value of \(icr\) is then mapped to build Musgrave filters (find_icr()):

    • For quarterly data, if the length is 5, then \(icr = 0.001\); otherwise, \(icr = 4.5\).

    • For other frequencies, if the length is less than or equal to 9, then \(icr = 1.0\).

    • Else, if the length is less than or equal to 13, then \(icr = 3.5\).

    • Else, \(icr = 4.5\).

Examples

if (FALSE) { # rjd3jars::check_java_version(silent = TRUE)
x11_trend_selection(cars_registrations)
find_icr(length = 13, freq = 12)
}