  This paper presents a statistical methodology for analyzing a complex
phenomenon in which deterministic and scaling components are superimposed. Our
approach is based on the wavelet multiresolution analysis combined with the
scaling analysis of the entropy of a time series. The wavelet multiresolution
analysis decomposes the signal in a {\it scale-by-scale} manner. The {\it
scale-by-scale} decomposition generates smooth and detail curves which are
evaluated and studied. A wavelet-based smoothing filtering is used to estimate
the daily birth rate and conception rate during the year. The scaling analysis
is based upon the Diffusion Entropy Analysis (DEA). The joint use of the DEA
and the wavelet multiresolution analysis allows: 1) the separation of the
deterministic and, therefore, non-scaling component from the scaling component
of the signal; 2) the determination of the stochastic information
characterizing the teen birth phenomenon at each time scale. The daily data
cover the number of births to teens in Texas during the period from 1964 to
1999.
