Compute the smoothness of trend-cycle estimates using Picard and Matthews (2006) definition.
Details
There are several definitions or criteria of smoothness. The measure of smoothness used here is defined as: $$ 100 \times \sqrt{ \frac{ \sum_t [(TC_t - TC_{t-1})/TC_{t-1}]^2 }{ \sum_t [(SA_t - SA_{t-1})/SA_{t-1}]^2 } } $$ This represents a measure of the month-to-month percentage change in the trend-cycle. The smaller the smoothness number is, the smoother the trend-cycle.
References
Picard, Frédéric et Steve Matthews (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/p icard_ssc2016.pdf>.