How can I detect significant changes in my data?

Question

I have a dataset like this:

> df1
                      date               count
1                  2012-07-01          11.749347
2                  2012-08-01           3.492433
3                  2012-09-01           4.539559
4                  2012-10-01          14.429109
5                  2012-11-01           6.203474
6                  2012-12-01          11.570248
7                  2013-01-01           7.952286
8                  2013-02-01          16.265912
9                  2013-03-01          21.481481
10                 2013-04-01          16.643551
11                 2013-05-01          18.849206
12                 2013-06-01           7.188498
13                 2013-07-01          25.343643
14                 2013-08-01          22.260274
15                 2013-09-01          27.531957
16                 2013-10-01          27.838428
17                 2013-11-01          31.343284
18                 2013-12-01          55.105348

As you can see in the plot, I have increasing and decreasing parts.

My questions now are : 1) How can I detect significant level changes in my data?

I already ran a MinMax function which gives me local mins and maxs, but do you have any other ideas how I could group my data into significant intervals which can be seen by human eye? I am searching for multilpe ways to do so.

Answer 1

Looking for "outliers" will not give you the appropriate answer because you have a trend. Moreover the trend is not linear, so the answer will depend on the trend model.

What you should do is :

(1) fit the trend. I choose a logistic function with a MAD but an exponential with LSE growth would have lead the same results

(2) compute the residuals $e(t)$ as the observed data minus the model.

(3) search for the outliers on the residuals. I tool Tuckey's fence with $|e(t)|$ greater than 1.5 times the interquartile.

The attached graph shows that obviously you should choose an exponential growth with a multiplicative error, thus minimizing the MAPE and computing the errors in percentage.

Answer 2

I endorse AlainD's answer. I would provide your audience with two charts, a scatterplot, without lines, and a trend plot. I like the loess method. Here's how it looks with ggplot

> library(ggplot2)
> p <- ggplot(data = df1, aes(x=date,y=count)) + geom_point() + geom_smooth()
> p