How to interpret decomposition plot and check for seasonality

Question

I'm new to this and I have a question about the results that I get from checking whether my data contains seasonality or not. I have a csv file which contains date, period and year. However, R reads the date as a factor and I didn't know how to deal with is. So I extracted the frequencies per month, so I have very little points now. The point contain the frequencies of the years 2012 and 2013.

My code:

k <- c(1110,989,1141,674,790,739,842,1004,751,765,1246,1045,
       1106,1078,1012,965,978,991,856,703,784,639,821,518)

z <- ts(k, start =c(2012,1), frequency =12)

plot(decompose(z))

I really don't know how to read this an whether I can draw a conclusion about seasonality by this methods or not.

Answer 1

Smoothing procedures like that implemented in decompose are not intended to check for the presence of seasonality (or at least it is not straightforward to use it to that end). You should first use other methods to decide whether seasonality is present (for example a plot of the autocorrelation, periodogram, statistical tests,...). If you conclude that seasonality is present then it makes sense to apply decompose on the data. See this post.

Answer 2

I see a strong seasonality. Look at the attached picture: I split your time series in two parts (2012 and 2013), and then I drew three squares (A,B,C) representing three four-months-periods for each year. Notice that the pattern inside squares A,B, and C belonging to different years is very similar. Such a similarity indicates a strong seasonality in your data.