Change-Point Detection Using the Conditional Entropy of Ordinal Patterns

. 2018 Sep 14;20(9):709. doi: 10.3390/e20090709

Algorithm 2 Detecting multiple change-points

Input: sequence

π = {(π (k))}_{k = d}^{L}

of ordinal patterns of order d, nominal probability

α

of false alarm.
Output: estimates of the number

{\hat{N}}_{st}

of stationary segments and of their boundaries

{({\hat{t}}_{k}^{*})}_{k = 0}^{{\hat{N}}_{st}}

1:
functionDetectAllCP( $π$ , $α$ )
2:
${\hat{N}}_{st} \leftarrow 1$ ; ${\hat{t}}_{0}^{*} \leftarrow 0$ ; ${\hat{t}}_{1}^{*} \leftarrow L$ ; $k \leftarrow 0$ ▷ Step 1
3:
repeat
4:
${\hat{t}}^{*}$ ← DetectSingleCP( ${(π (l))}_{l = {\hat{t}}_{k}^{*} + d}^{{\hat{t}}_{k + 1}^{*}}$ ), $2 α$ ;
5:
if ${\hat{t}}^{*} > 0$ then
6:
Insert ${\hat{t}}^{*}$ to the list of change-points after ${\hat{t}}_{k}^{*}$ and renumber change-points ${\hat{t}}_{k + 1}^{*}, \dots, {\hat{t}}_{{\hat{N}}_{st}}^{*}$ ;
7:
${\hat{N}}_{st}$ ← ${\hat{N}}_{st} + 1$ ;
8:
else
9:
k ← $k + 1$ ;
10:
end if
11:
until $k < {\hat{N}}_{st}$ ;
12:
k ← 0; ▷ Step 2
13:
repeat
14:
${\hat{t}}^{*}$ ← DetectSingleCP( ${(π (l))}_{l = {\hat{t}}_{k}^{*} + d}^{{\hat{t}}_{k + 2}^{*}}$ , $α$ );
15:
if ${\hat{t}}^{*} > 0$ then
16:
${\hat{t}}_{k + 1}^{*}$ ← ${\hat{t}}^{*}$ ;
17:
k ← $k + 1$ ;
18:
else
19:
Delete ${\hat{t}}_{k + 1}^{*}$ from the change-points list and renumber change-points ${\hat{t}}_{k + 2}^{*}, \dots, {\hat{t}}_{{\hat{N}}_{st}}^{*}$ ;
20:
${\hat{N}}_{st}$ ← ${\hat{N}}_{st} - 1$ ;
21:
end if
22:
until $k < {\hat{N}}_{st} - 1$ ;
23:
return ${\hat{N}}_{st}, {({\hat{t}}_{k}^{*})}_{k = 0}^{{\hat{N}}_{st}}$ ;
24:
end function