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@@ -85,16 +85,18 @@ Although the ITS analysis takes data density variability and seasonality into ac
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\subsection{A synthetic example}
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The diagram in figure \ref{itsexample} is generated by the following algorithm:
%3 segment example like it will be used later
% with lower sentiment first and higher sentiment after the change
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For demonstration purposes, this section shows how to create a synthetic example for ITS. The example has 3 segments, equal to the number of segments that will be used in the analysis in the next sections. In this example the sentiment is lower before the change occurs and high after the change has occurred. This example also includes data density variablily, i.e., there are a different amount of data points for each month. The example is shown visually in figure \ref{itsexample} is generated by the following algorithm:
\begin{itemize}
\item Select base values: before the change choose a base value of 0.10 and after the change choose a base value of 0.15
\item Add noise: add a random value in $[0, 0.05)$ to the base value for each month
\item Choose sample size: choose a random sample size in $[200, 400)$ for each month and duplicate the value from the previous step by the sample size in each month respectively
\item Select time frame: for instance, 15 months before and after the change
\item Select base values: before the change choose a base value of $0.10$ and after the change choose a base value of $0.15$
\item Add noise: add a random value in $[0, 0.05)$ to the base value for each month respectively
\item Choose sample size (data density): choose a random sample size in $[200, 400)$ for each month and duplicate the value from the previous step by the sample size in each month respectively
\item Compute the ITS: while taking data density variability into account
\end{itemize}
This algorihm generates an ITS where the line before the change is on a lower level than the line after the change. However, this algorithm does not control the slopes of the lines before and after the change. The slopes of the lines in \ref{itsexample} are random. The algorithm could be extended to also control the slopes of the lines, however, for demonstration purposes this is enough.
This algorihm generates an ITS where the line before the change is on a lower level than the line after the change. However, this algorithm does not control the slopes of the segments before and after the change. The slopes of the lines in \ref{itsexample} are random. The algorithm could be extended to also control the slopes of the lines, however, for demonstration purposes in this thesis this is enough.
\begin{figure}