During the outbreak of an epidemic disease, for example, the severe acute respiratory syndrome (SARS), the number of daily infected cases often exhibit multiple trends: monotone increasing during the growing stage, stationary during the stabilized stage and then decreasing during the declining stage. Lam first proposed modelling a monotone trend by a geometric process (GP) [X(i), i=1,2,...] directly such that [a(i-1)X(i), i=1,2,...] forms a renewal process for some ratio a>0 which measures the direction and strength of the trend. Parameters can be conveniently estimated using the LSE methods. Previous GP models limit to data with only a single trend. For data with multiple trends, we propose a moving window technique to locate the turning point(s). The threshold GP model is fitted to the SARS data from four regions in 2003.
Copyright 2005 John Wiley & Sons, Ltd.