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consisting of N publication years, from year Y to year Y 1 N 2 1 (the
columns) and M citation years, from year Y to year Y 1 M 2 1 (the rows).
Hence the p-c matrix is an M 3 N-matrix. These N years form the publi-
cation window, while the M years form the citation window of interest.
For specific terms in a sequence smaller windows will often be used. We,
moreover assume that the number of columns is at most equal to the
number of rows: N # M. We keep the p-c matrix fixed and study series
of citation indicators derived from this set. We define general time series
of indicators and characterize what they say about the set of publications.
Recall that citations are always drawn from a pool, such as the WoS,
Scopus, a local database or subsets thereof. We will further assume that
this pool is known and will not consider this aspect anymore.

7.11.2 Types of Time Series of Citation Indicators
We will explain the construction of different time series and their visuali-
zations in p-c matrices. In these visualizations the shaded areas contain
the citation data that are added in order to obtain one element in the
time series. Series (s k ) k will be called chronological if the index k increases
with time (years) and antichronological if it increases with decreasing years.
The first series is a citation cumulated, publication-chronological time
series. The first term of this series is the sum of all citations received by
publications of the year Y, during the period Y to Y 1 M 2 1; the second
term is the sum of all citations received by publications of the year Y 1 1,
during the period Y 1 1toY 1 M 2 1; and so on. This procedure leads
to a series of diachronous indicators, making use of all data available in
the p-c matrix. If year Y 1 M 2 1 is the latest year for which data are
available this is a natural approach, although publication years are treated
unevenly (they contribute differently). Cells used in the calculation of
one term of this series are shaded in Table 7.8. In this way the calcula-
tions of four terms are illustrated in Table 7.8, one below the other. For
the p-c matrix shown in Table 7.8 the resulting series is: (22,13,23,19).
This type of time series has been provided for the Hirsch index of the
Journal of the American Society for Information Science in (Rousseau, 2006b).
It was suggested that a normalization with respect to the number of
published articles was preferable.
The second time series is a citation cumulated, publication cumulating
chronological time series. It is similar to the first type but uses cumulative
data. This time series, and also the previous one, was used in (Liu et al.,