Measure Smoothness of Trend-Cycle Estimates

Computes the smoothness ratio of trend-cycle estimates relative to the seasonally adjusted series following Picard and Matthews (2016).

Usage

smoothness(x)

Arguments

x

An object of class "tc_estimates".

Value

A numeric value representing the smoothness index of the trend-cycle estimates.

Details

Smoothness is evaluated as the ratio of month-to-month growth rate variances: $$ 100 \times \sqrt{ \frac{ \sum_t \left( \frac{TC_t - TC_{t-1}}{TC_{t-1}} \right)^2 }{ \sum_t \left( \frac{SA_t - SA_{t-1}}{SA_{t-1}} \right)^2 } } $$

This metric quantifies the relative variability of the trend-cycle compared to the seasonally adjusted series. A lower value indicates a smoother trend-cycle.

References

Picard, F., & Matthews, S. (2016). The Addition of Trend-Cycle Estimates to Selected Publications at Statistics Canada. Proceedings of the Survey Methods Section, Statistical Society of Canada (SSC) Annual Meeting. https://ssc.ca/sites/default/files/imce/pdf/picard_ssc2016.pdf

Examples

if (FALSE) { # rjd3jars::check_java_version(silent = TRUE)
x <- french_ipi[, "manufacturing"]
tc_clf <- clf_smoothing(x)
tc_henderson <- henderson_smoothing(x)
smoothness(tc_clf)
smoothness(tc_henderson)
}