My knowledge of time-series analysis is limited. So far I have only assessed whether there was a seasonality in my time series data with the assumption of monotonic trend. To test that I would have performed either the Cox-Stewart Test or (preferably) tested for auto-regression considering an additional variable reflecting the distribution of the months (1 to 12, and comparing it to a second model with a meaningless variable going for instance from 1 to 13). However I would need now to test my time series data (divided in months, over 10 years approx) for a seasonality which would allow data not only to have a monotonic pattern but also a sinusoidal pattern. How could I do that? I normally use Stata but might do it in R as well (if necessary...)

  • $\begingroup$ sinusoidal pattern = seasonality. $\endgroup$ – Romain Jan 17 '16 at 18:27
  • $\begingroup$ Does the period of the sinusoid coincide with the seasonal period? Then @Romain is right, the sinusoid would coincide with the seasonal pattern. If not, then just include seasonal dummies or seasonal Fourier terms (sine and cosine waves) extra to the non-seasonal sine wave, and test their joint significance (excluding the non-seasonal sine wave). $\endgroup$ – Richard Hardy Jan 17 '16 at 18:47
  • $\begingroup$ Stewart should be Stuart. $\endgroup$ – Nick Cox Jan 18 '16 at 1:29

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