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I'm working on housing data set for a project for a undergraduate time series course. I'm trying to see if there is seasonality in the data. I used the following commands but do not know how to read the graphs to see if there is seasonality. 

spec.pgram(data) #non-parametric estimate of the spectrum
spec.pgram(data, log="no")

enter image description here

This is the data set I'm working with. http://www.quandl.com/FRED/HOUST-Housing-Starts-Total-New-Privately-Owned-Housing-Units-Started

kjetil b halvorsen
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user52760
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  • Try the decompose() function in R? Alternatively, looks at the ACF and PACF plots. If you find recurring spikes, you have seasonality. – Arun Jose Jul 25 '14 at 05:14
  • How would I know if it's seasonal from the decompose function? – user52760 Jul 25 '14 at 05:30
  • Decompose breaks up your series into seasonal, trend and error components. You can plot this and verify seasonality. However, the ACF would be a better bet. – Arun Jose Jul 25 '14 at 05:34
  • The ACF has a slow decay. But no jumps. http://imgur.com/TucNJFN – user52760 Jul 25 '14 at 06:04
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    Based on that plot, almost no evidence of seasonality and it is evident you have non-stationary data. – Arun Jose Jul 25 '14 at 07:41
  • Thanks. Both the ACF and the plotted decomposed graph seems to support that. Seems like difference once makes the data stationary. But once I difference it there seems to be seasonality. http://imgur.com/jH4P4iI – user52760 Jul 25 '14 at 09:06
  • There are no peaks at the seasonal frequencies, therefore as @Arun Jose said there is no evidence of seasonality. You may also see this post for some details about the interpretation of this plot, in particular the x-axis. How do you check for seasonality in the differenced series? I don't see any peaks at the seasonal frequencies in this plot spectrum(diff(x), span=c(3,3)). – javlacalle Jul 26 '14 at 12:05
  • That seems contradictory to the intuition doesn't it? Considering it is housing data wouldn't you expect there to strong seasonality? – user52760 Jul 26 '14 at 23:23
  • After looking more closely to the source of the data this is not contradictory at all. The description says "Seasonally Adjusted", so the seasonal pattern that you expect has been removed. You could search in the data base and see if the not seasonally adjusted data are also provided. – javlacalle Jul 28 '14 at 13:29

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