Journal of Applied Mathematics and Decision Sciences
Volume 2006 (2006), Article ID 34784, 12 pages

The smoothness criterion as a trend diagnostic

P. Fogarty and N. C. Weber

School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia

Received 12 January 2005; Accepted 1 March 2005

Copyright © 2006 P. Fogarty and N. C. Weber. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The smoothness criterion is used in the design of symmetric moving average trend filters in time series and in graduation in actuarial studies. This measure of smoothness is used to motivate a diagnostic for determining the order of local polynomial trend.