Given an OTS of length \(T\) with range \(\mathcal{S}=\{s_0, s_1, s_2, \ldots, s_n\}\) (\(s_0 < s_1 < s_2 < \ldots < s_n\)),
\(\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}\), the function
constructs the binarized time series, which is defined as
\(\overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, \ldots, \overline{\boldsymbol Y}_T\}\),
with \(\overline{\boldsymbol Y}_k=(\overline{Y}_{k,0}, \overline{Y}_{k,1},\ldots, \overline{Y}_{k,n})^\top\)
such that \(\overline{Y}_{k,i}=1\) if \(\overline{X}_k=s_i\) (\(k=1,\ldots,T,
, i=0,\ldots,n\)). The binarized series is constructed in the form of a matrix
whose rows represent time observations and whose columns represent the
states in the original series.