Analyzing Spatio-temporal Data: Empirical and Statistical Approaches - Spatio-temporal Approaches - page 93

first date. We will not present in detail here the whole tree and the associated
thresholds. The objective of this example was mainly to illustrate the difficulty in
tracking a composite object resulting from a process of construction established at
time t. The process itself mobilizing evaluations of interactions between the places
makes it difficult to construct a concrete and stable referential in time. In this case,
the classification procedure allows a supervised procedure to be put in place, to
identify change a priori , and not to assess it a posteriori on the basis of the
comparison of two states. Figure 3.12 illustrates the few transformations that have
been identified: overall, the main tendency is toward stability. However, a few
extensions should be noted: they concern the most dynamic centers, which extend in
the direction of the satellite towns [BER 11a].
Figure 3.12. Identifying composite objects' changes: employment
centers in the Parisian urban area (source: [BER 11a])
3.3.3. “ Unfolded” time and forecast
The analysis of observations made on regularly spaced dates (for example, the
population of cities each year) refers in statistics to a domain named “time series” or