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Some context: I'm working with deforestation areas. An research institute provides time series data of deforested areas (in km²) in two ways: monthly and annual. Each one of them is obtained by a different methodology (like different satellites, image resolutions, etc). So, in my study, I selected the years from 2009-2016, obtaining 8 observations (one for year 2009, one for 2010, ...) in the annual series and 96 in the monthly series (jan-2009, feb-2009, ..., dec-2016). Since they're different methodologies, the monthly one doesn't provide the exact number of the annual series if we add up them.

My question is: Are there any ways/tests to show that the annual time series can share the same information (like periodicity/seasonality) as the monthly one?

What I have found so far:

a. I started studying time series recently using the R software and found the DTW (Dynamic Time Warping) package. Is searching for similarities using the short series as query and the other as a reference a good idea in this case?

b. I also found some dimensionality reductions like Piecewise regression and Piecewise Aggregate Approximation so I can reduce the monthly time series. Can this help with the comparison?

c. ARMA models were discussed here, but doing that was not indicated.

Thanks in advance for any help provided.

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  • $\begingroup$ If you are after seasonality (which means frequencies at least 1/year), and you find this in the monthly data, then you can be sure that the annual data won't contain it (Nyquist theorem requires you to sample at least twice a year). Or am I missing something in what you are trying to do? $\endgroup$ – Sextus Empiricus Jun 14 '17 at 6:55
  • $\begingroup$ Hello, thanks for replying. It's just that. I will work with images later, so, working with 8 images (one per year) would be easier than 96 (one per month) using the years of 2009, 2010, ..., 2016. Then I thought it was possible to compare both time series and verify if the short one could be used instead of the longer one without losing information like periodicity, seasonality, cycles, etc. $\endgroup$ – Kol Rocket Jun 14 '17 at 22:45
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If you want to analyze the different periodicity of your data sets, you may check the decompose() function within the R stats package.

From a periodicity standpoint, an annual data set will convey a lot less info than a monthly data set.

And, your research objective should play a role in your decision of which data set to chose. If you are interested in seasonality effect, you need monthly data. Even if you are not looking for seasonality effect, you may prefer the monthly data to get an adequate sample for your time series.

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