Approximations of Time Series

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.