ALGORITHM 1: Permutation-based Change Detection(X)

$$\begin{array}{cc}\hfill & \text{Input:}X=\text{time series data}\hfill \\ \hfill & \text{Output: Vector}V\text{of (distance, significance) pairs}\hfill \\ \hfill & \text{Initialize:}n=7\#\text{window length in number of days}\hfill \\ \hfill & \text{Initialize:}i=1;j=i+n\hfill \\ \hfill & \mathbf{for}\mathbf{each}\text{pair of windows},W_i,W_{j\subseteq }X\mathbf{do}\hfill \\ \hfill & W_i=\mathrm{X}[i:i+n]\hfill \\ \hfill & W_j=\mathrm{X}[j:j+n]\hfill \\ \hfill & k=0;N=1000\hfill \\ \hfill & C=\text{KL}\_\text{Divergence}(W_i,W_j)\hfill \\ \hfill & V^{\ast }=\text{vector of length}N\hfill \\ \hfill & \mathbf{while}k<N\mathbf{do}\hfill \\ \hfill & W_i^{\ast },W_j^{\ast }=\text{Shuffle time intervals of}{W}_i\text{and}{W}_j\hfill \\ \hfill & C^{\ast }=\text{KL}\_\text{Divergence}(W_i^{\ast },W_j^{\ast })\hfill \\ \hfill & V^{\ast }=\text{append}(V^{\ast },C^{\ast })\hfill \\ \hfill & k=k+1\hfill \\ \hfill & \mathbf{end}\mathbf{while}\hfill \\ \hfill & sig=\text{BoxplotOutlierDetection}(C,V^{\ast })\hfill \\ \hfill & V=\text{append}(V,(C,sig))\hfill \\ \hfill & j=j+n\hfill \\ \hfill & \mathbf{end}\mathbf{for}\hfill \\ \hfill & \mathbf{return}V\hfill \end{array}$$