Given a OTS of length \(T\) with range \(\mathcal{S}=\{s_0, s_1, \ldots, s_n\}\),
\(\overline{X}_t=\{\overline{X}_1,\ldots, \overline{X}_T\}\), and
the cumulative binarized time series, which is defined as
\(\overline{\boldsymbol Y}_t=\{\overline{\boldsymbol Y}_1, \ldots, \overline{\boldsymbol Y}_T\}\),
with \(\overline{\boldsymbol Y}_k=(\overline{Y}_{k,0}, \ldots, \overline{Y}_{k,n-1})^\top\)
such that \(\overline{Y}_{k,i}=1\) if \(\overline{X}_k \leq s_i\) (\(k=1,\ldots,T
, i=0,\ldots,n-1\)), the function computes the estimated TMCQC given by
$$\widehat{\Psi}_2^m(l)=\frac{1}{n}\sum_{i=0}^{n-1}\int_{0}^{1}\widehat{\psi}^\rho_{i}(l)^2d\rho,$$ where
\(\widehat{\psi}_{i}^\rho(l)=\widehat{Corr}\big(Y_{t,i}, I(Z_{t-l}\leq q_{Z_t}(\rho)) \big)\), with
\(\overline{Z}_t=\{\overline{Z}_1,\ldots, \overline{Z}_T\}\) being a
\(T\)-length real-valued time series, \(\rho \in (0, 1)\) a probability
level, \(I(\cdot)\) the indicator function and \(q_{Z_t}\) the quantile
function of the corresponding real-valued process. If features = TRUE, the function
returns a vector whose components are the quantities \(\int_{0}^{1}\widehat{\psi}^\rho_{i}(l)^2d\rho\),
\(i=0,1, \ldots,n-1\).