Changepoint PELT penalty

Question

I am analyzing changes in unique users' ratings for different movies in time. In order to find changepoints in time, I am using the 'changepoint' package and the PELT method. I understand that there are different types of penalties, however, I am still unsure which one to use. I tried to make an elbow plot to see the optimal number of changes, but somehow it does not work. My question is how can I set the optimal penalty for my example? Also, for the interpretation, are all changepoints significant? Is there a way to prove significance?

Here is what I have so far, based on, for example, the movie "Inception".

My data: timestamp_date = date; cummean = all ratings for the day:

timestamp_date  cummean
18-07-2010  4.15384615
19-07-2010  4.23809524
20-07-2010  4.23880597
21-07-2010  4.24390244
22-07-2010  4.19387755
23-07-2010  4.21186441
24-07-2010  4.23758865
25-07-2010  4.28804348
26-07-2010  4.32126697
27-07-2010  4.34063745
28-07-2010  4.36330935
29-07-2010  4.35521886
30-07-2010  4.35448916
31-07-2010  4.34005764
1-08-2010   4.34741144
2-08-2010   4.35604113
3-08-2010   4.34725537
4-08-2010   4.33073497
5-08-2010   4.34051724
6-08-2010   4.34114053
7-08-2010   4.3467433
8-08-2010   4.32909091
9-08-2010   4.32901554
10-08-2010  4.32171799
11-08-2010  4.32316119
12-08-2010  4.32375189
13-08-2010  4.32532751
14-08-2010  4.32932011
15-08-2010  4.32855191
16-08-2010  4.33266932
17-08-2010  4.33246415
18-08-2010  4.33312102
19-08-2010  4.32982673
20-08-2010  4.33212121
21-08-2010  4.33195755
22-08-2010  4.33198614
23-08-2010  4.33370913
24-08-2010  4.3342511
25-08-2010  4.33441208
26-08-2010  4.33439153
27-08-2010  4.33541018
28-08-2010  4.331643
29-08-2010  4.32954545
30-08-2010  4.32992203
31-08-2010  4.330468
1-09-2010   4.33002833
2-09-2010   4.32679739
3-09-2010   4.32763401
4-09-2010   4.33091568
5-09-2010   4.33081033
6-09-2010   4.3289358
7-09-2010   4.33072917
8-09-2010   4.33104631
9-09-2010   4.33347422
10-09-2010  4.33430962
11-09-2010  4.33251029
12-09-2010  4.33292782
13-09-2010  4.33360129
14-09-2010  4.33359936
15-09-2010  4.33307024
16-09-2010  4.33268025
17-09-2010  4.33256528
18-09-2010  4.33358548
19-09-2010  4.33247232
20-09-2010  4.33734088
21-09-2010  4.33758621
22-09-2010  4.34044715
23-09-2010  4.34026846
24-09-2010  4.33878505
25-09-2010  4.33542631
26-09-2010  4.33409836
27-09-2010  4.33268482
28-09-2010  4.3332256
29-09-2010  4.33451157
30-09-2010  4.33545108
1-10-2010   4.33470032
2-10-2010   4.33550995
3-10-2010   4.33374384
4-10-2010   4.33455882
5-10-2010   4.33638026
6-10-2010   4.33704819
7-10-2010   4.33871933
8-10-2010   4.33881579
9-10-2010   4.33718861
10-10-2010  4.33931725
11-10-2010  4.34020918
12-10-2010  4.33927545
13-10-2010  4.33714286
14-10-2010  4.33730835

My code:

inds <- seq(as.Date("2010-07-18"), as.Date("2010-10-14"), by = "day")
myts <- ts(inception$cummean, start = c(2010, as.numeric(format(inds[1], "%j"))), frequency = 365)

#single changepoint: method AMOC
cpt <- changepoint::cpt.meanvar(myts)
cpts(cpt)
cpts.ts(cpt)
param.est(cpt)
plot(cpt)
summary(cpt)

#multiple changepoints: method PELT 
mcpt <- changepoint::cpt.meanvar(myts, method = "PELT")
cpts(mcpt)
cpts.ts(mcpt)
param.est(mcpt) 
ncpts(mcpt) 
plot(mcpt)
summary(mcpt)

Thank you!!

Answer 1

I tried to make an elbow plot to see the optimal number of changes, but somehow it does not work.

The following code works for me:

mcpt <- changepoint::cpt.meanvar(myts, method = "PELT",penalty="CROPS",pen.value=c(0,200)) plot(mcpt,diagnostic=T)

I would then say that there were 3 changepoints based on this graph and a plot of the original time series.

plot(mcpt,ncpts=3)

You can then debate whether the final changepoint is "relevant" to the application at hand or not. The inflated penalty is required because there is dependence in the data. The core assumption of the default "Normal" cost function for cpt.meanvar() is that the data are independent.