# Univariate time series: How to determine a periodogram and how to interpret?

I have the following univariate time series:

Month/Year  ItemsSold
01/2005 0
02/2005 0
03/2005 0
04/2005 0
05/2005 3
06/2005 0
07/2005 1
08/2005 3
09/2005 1
10/2005 0
11/2005 1
12/2005 2
01/2006 0
02/2006 0
03/2006 1
04/2006 4
05/2006 0
06/2006 1
07/2006 2
08/2006 0
09/2006 0
10/2006 0
11/2006 0
12/2006 1
01/2007 3
02/2007 0
03/2007 0
04/2007 2
05/2007 2
06/2007 9
07/2007 2
08/2007 5
09/2007 8
10/2007 1
11/2007 3
12/2007 3
01/2008 2
02/2008 2
03/2008 11
04/2008 6
05/2008 0
06/2008 4
07/2008 6
08/2008 0
09/2008 0
10/2008 0
11/2008 3
12/2008 0
01/2009 5
02/2009 2
03/2009 2
04/2009 2
05/2009 3
06/2009 40
07/2009 5
08/2009 4
09/2009 3
10/2009 0
11/2009 4
12/2009 1
01/2010 1
02/2010 0
03/2010 26
04/2010 0
05/2010 3
06/2010 46
07/2010 15
08/2010 1
09/2010 3
10/2010 1
11/2010 20
12/2010 0
01/2011 0
02/2011 0
03/2011 10
04/2011 0
05/2011 0
06/2011 0
07/2011 31
08/2011 1
09/2011 0
10/2011 5
11/2011 0
12/2011 2
01/2012 0
02/2012 0
03/2012 6
04/2012 0
05/2012 1
06/2012 0
07/2012 76
08/2012 0
09/2012 3
10/2012 0
11/2012 1
12/2012 0
01/2013 0
02/2013 0
03/2013 2
04/2013 0
05/2013 0
06/2013 4
07/2013 0
08/2013 0
09/2013 0
10/2013 1
11/2013 0
12/2013 8
01/2014 0
02/2014 0
03/2014 2
04/2014 14
05/2014 19
06/2014 0
07/2014 2
08/2014 7
09/2014 2
10/2014 0
11/2014 0
12/2014 0
01/2015 3
02/2015 0
03/2015 0


First I have read the column ItemsSold into a vector datalist:

datalist
[1]  0  0  0  0  3  0  1  3  1  0  1  2  0  0  1  4  0  1  2  0  0  0  0  1  3  0  0  2  2  9  2
[32]  5  8  1  3  3  2  2 11  6  0  4  6  0  0  0  3  0  5  2  2  2  3 40  5  4  3  0  4  1  1  0
[63] 26  0  3 46 15  1  3  1 20  0  0  0 10  0  0  0 31  1  0  5  0  2  0  0  6  0  1  0 76  0  3
[94]  0  1  0  0  0  2  0  0  4  0  0  0  1  0  8  0  0  2 14 19  0  2  7  2  0  0  0  3  0  0

> length(datalist)
[1] 123


That is the raw data plotted:

Using the package TSA from CRAN I get:

periodogram(datalist)


My question is: What does it say about the time series I got? And what further analysis can I do (e.g. Fourier transform, etc.)?

• First part on did you use R correctly is off-topic here. Second part on what else you could do with a time series is too broad. Please read advice on the Help Center on what is on-topic and a good question. – Nick Cox Feb 20 '15 at 18:52
• Okay. Maybe you can help me answering what question of what the periodogram says about the time series I got. – user69442 Feb 20 '15 at 19:03
• If you think the comment is fair, you should re-edit the question and give more background, not use the comments to try to change the question on the fly. (But a quick glance makes me wonder why and whether a periodogram should be expected to be helpful at all.) – Nick Cox Feb 20 '15 at 19:20
• This Q doesn't strike me as really about how to use R, although it is somewhat couched in those terms. Although I don't know TS well enough, I suspect the 'what else' part is if there is something specific & obvious that follows this step in TS analyses, & not just what kinds of things can be done in an unconstrained sense. The 'how to interpret the periodogram' part is surely on-topic here. I am voting to leave open. – gung Feb 20 '15 at 19:24
• The question could be improved then by plotting the raw data (so we don't have to) and giving a tentative interpretation. – Nick Cox Feb 20 '15 at 19:37