Load `bcpa`

, and a few other handy packages:

```
require(magrittr)
require(lubridate)
require(bcpa)
```

We simulate some data with four phases / three change points: surface to medium to deep to surface, that occur at fixed times.

```
<- 100
n.obs = (Sys.time() - dhours(runif(n.obs, 0, n.obs))) %>% sort
time
<- 50; d2 <- 100
d1 <- 25; t2 <- 65; t3 <- 85
t1 <- 1; sd2 <- 5; sd3 <- 10
sd1
<- difftime(time, min(time), units="hours") %>% as.numeric
dtime <- cut(dtime, c(-1, t1, t2, t3, 200), labels = c("P1","P2","P3","P4"))
phases <- c(0,d1,d2,0)[phases]
means <- c(sd1,sd2,sd3,sd1)[phases]
sds <- rnorm(n.obs,means, sds)
depth # make all depths positive!
<- abs(depth)
depth <- data.frame(time, depth) mydata
```

The structure of the data is very simple:

`head(mydata)`

```
## time depth
## 1 2022-05-23 08:36:42 0.32192527
## 2 2022-05-23 09:13:09 0.78383894
## 3 2022-05-23 09:40:42 1.57572752
## 4 2022-05-23 10:08:49 0.64289931
## 5 2022-05-23 10:24:15 0.08976065
## 6 2022-05-23 11:44:36 0.27655075
```

Plot simulated depth data

`with(mydata, plot(time, depth, type = "o"))`

Perform the window sweep. Note that you specify the response variable (`depth`

) and the time variable (`time`

):

`<- WindowSweep(mydata, variable = "depth", time.var = "time", windowsize = 25, windowstep = 1, progress=FALSE) depth.ws `

Here are some plots and the summary of the change point analysis:

`plot(depth.ws, ylab = "Depth (m)")`

`plot(depth.ws, type = "flat", cluster = 8, ylab = "Depth (m)")`

`ChangePointSummary(depth.ws, cluster = 8)`

```
## $breaks
## X1 middle size modelmode middle.POSIX
## 1 1 25.46224 27 4 2022-05-24 09:58:01
## 2 2 62.47157 18 4 2022-05-25 22:46:30
## 3 3 84.46078 12 4 2022-05-26 20:34:54
##
## $phases
## t.cut mu.hat s.hat rho.hat t0 t1 interval
## 1 (-1,25.5] 3.681865 11.256694 1.4733085237 -1.00000 25.46224 26.46224
## 2 (25.5,62.5] 50.063357 4.367361 0.0005596285 25.46224 62.47157 37.00933
## 3 (62.5,84.5] 91.941686 17.048889 0.0883214493 62.47157 84.46078 21.98921
## 4 (84.5,98.9] 6.434163 22.852427 0.0613947945 84.46078 98.86528 14.40450
```

This is a pretty artificial example, but it works well.

## Comments

The BCPA was originally formulated to analyze irregular movement data collected on marine mammals, but in essence it simply reduced movement data (X-Y-Time) to a univariate time-series. There are - in my opinion - better (i.e. more informative and more robust) tools for dealing with movement data specifically, (e.g. at https://github.com/EliGurarie/smoove), but the BCPA might still be useful for irregular univariate time series. An example (again from marine mammals) is depth data. A recent update to BCPA makes this analysis somewhat smoother. Here is an example on simulated data.

Note - to date this is available only on the GitHub version of BCPA, i.e. the first step is:

The code for this example can also be found in the help file for the

`WindowSweep()`

function.