Algorithm 2. sw-PCAR($W_i$, $W_j$, $N$)

$$\begin{array}{cc}\hfill & 1:\text{Input:}{W}_i,W_j=\text{two windows of time series data}\hfill \\ \hfill & 2:\text{Input:}N=\text{number of permutaions}\hfill \\ \hfill & 3:\text{Output:}CS=\text{change score}\hfill \\ \hfill & 4:\text{Output:}sig=(\text{Boolean})\text{significance of}CS\hfill \\ \hfill & 5:\text{Initialize:}k=0\hfill \\ \hfill & 6:\text{Initialize:}V\text{as a vector of length}N\hfill \\ \hfill & 7:\text{Compute}{\widehat{W}}_i,{\widehat{W}}_j\text{aggregate window}\hfill \\ \hfill & 8:\text{Compute}CS,\text{the KL distance between}{\widehat{W}}_i\text{and}{\widehat{W}}_j\hfill \\ \hfill & 9:\mathbf{while}k<N:\hfill \\ \hfill & 10:\text{Shuffle the time intervals of}{\widehat{W}}_i\text{and}{\widehat{W}}_j\hfill \\ \hfill & 11:\text{Generate new aggregate windows}{W}_i^{\ast }\text{and}{W}_j^{\ast }\hfill \\ \hfill & 12:\text{Compute the KL distance between}{W}_i^{\ast }\text{and}{W}_j^{\ast }\hfill \\ \hfill & 13:\text{Store resulting distance in}V\hfill \\ \hfill & 14:k=k+1\hfill \\ \hfill & \mathbf{end}\mathbf{while}\hfill \\ \hfill & 15:sig=\text{BoxplotOutlierDetection}(CS,V)(\text{see}\mathsf{Algorithm}3)\hfill \\ \hfill & 16:\mathbf{return}CS,sig\hfill \end{array}$$