A qualitative analysis refers to the
identification of the qualitative characteristics of a time
series, such as its periodicity, final periodicity or near
periodicity, convergence to the limit state, randomness, etc.
For such an analysis, methods of symbolic dynamics are
used, with the time series being represented as a sequence of
symbols from a finite alphabet. Such a representation of the
time series corresponds to the division of the state space of
the process into a finite number of parts, each of which is
denoted by a separate symbol. Thus, the symbolic
representation of the time series shows in which part of the
state space the process is at each moment.
The choice of the cardinality of the alphabet of the
symbols used affects the dependence between the
laboriousness of obtaining the results of the analysis of the
time series and their accuracy. To choose the cardinality of
the alphabet, it was proposed to use the method of analysis
of the entropy of words obtained using a sliding window of
variable length. Two approaches that differ in the criterion
of splitting are considered: coding of the time series levels
based on dividing the range of its values, and coding trends,
that is, changes in these values. A method for calculating the
entropy function is described. Decision rules are proposed
for obtaining various qualitative characteristics of symbolic
representations of time series based on the values of the
entropy function.