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I have a time series sampled in days and when I plot the amplitude vs time it looks like the signal is oscialating at an annual frequency. The series is 15 years long.

Is there a test I can use to test the significance of this frequency in the data? Meaning, test what is the probablity the oscilation is random.

I have used fft and autocorrelation to validate the existence of the period but these tests don't give a probablity measure as far as I know.

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2 Answers 2

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If I understood correctly you want to determine whether or not your series is plain white noise. If that's the case, the Ljung-Box test for autocorrelation should give you what you want.

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To test the significance of the annual frequency, you need a probability model. As Digio pointed out, Ljung-Box test would work to test for the existence of autocorrelation in the ts. But it wouldn't be clear if that's the annual or seasonal pattern in the data.

I am sure there are many ways to approach this problem. But if I were you, I would build a model, e.g., ARMA with an annual trend, and see if the coefficient for that annual trend is significant or not. I could also use information criterion to compare two models, one with an annual trend, the other one without an annual trend.

Hope it helps.

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