Table of Contents
ISRN Applied Mathematics
Volume 2011, Article ID 321683, 10 pages
Research Article

Approximations of Time Series

1Department of Surgery, University of Western Ontario, London, Canada N6A 5B7
2Department of Applied Mathematics, University of Western Ontario, London, Canada N6A 5B7

Received 14 June 2011; Accepted 18 July 2011

Academic Editors: A. J. Kearsley, M. Tabata, and F. Tadeo

Copyright © 2011 M. Brackstone and A. S. Deakin. 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.


A method is proposed to approximate the main features or patterns including interventions that may occur in a time series. Collision data from the Ontario Ministry of Transportation illustrate the approach using monthly collision counts from police reports over a 10-year period from 1990 to 1999. The domain of the time series is partitioned into nonoverlapping subdomains. The major condition on the approximation requires that the series and the approximation have the same average value over each subdomain. To obtain a smooth approximation, based on the second difference of the series, a few iterations are necessary since an iteration over one subdomain is affected by the previous iteration over the adjacent subdomains.