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I want to use Arima model for forecasting wind speed. I plot my data. enter image description here

Then I plot ACF and PACF. enter image description here

I used ADF test and KPSS test and they said that data are stationary and does not need differencing but in ACF plot we see Sinusoidal trend. Is it really stationary and does not need differencing?How we should know about seasonality?

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The wind speed is not very likely to increase (or decrease) without bounds, so it does not resemble a random walk. If there is a storm with strong wind, one would expect the storm to end after a reasonably short time rather than to continue forever or possibly intensify even more. On the other hand, if it is very quiet, one would expect some wind after a while (it is not likely to stay quiet forever). This points to a stationary nature of wind speed.

Meanwhile, seasonality is to be expected. I suppose there are at least two seasonal patterns, one with a period of 24 hours and another with a period of one year; perhaps there are more (check up with meteorologists). Thus examining seasonality in this data would make sense.

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  • $\begingroup$ How examing the seasonality?TNX $\endgroup$
    – saeed nj
    Aug 4, 2015 at 6:56
  • $\begingroup$ First, find out what the seasonal periods should be. The easy way is to check what the standard in the literature is. The hard way is trying to estimate the period. I would definitely opt for the former if possible. Second, you may use an ARIMA model with Fourier terms representing the seasonality. Find out more in Rob J. Hyndman's blog, for example, here and related posts (see links at the end of that post). $\endgroup$
    – Richard Hardy
    Aug 4, 2015 at 7:54

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