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I am analyzing the wind speed data which is a time series. The ARMA model works well on the data. But the same model fails to give good results when I difference the series. The Ljung-Box test gives p-value less than 0.05 (very close to 0). Does this mean that wind speed data may be considered a stationary time series?

Edit to the original post. The data was collected at 10 minute intervals. The plot is given below: enter image description here

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  • $\begingroup$ I don't think that can be answered in the abstract. It might well depend on geographical location, for instance. Seasonality on year and 24h cycles is a possibility. Can you show some plots? $\endgroup$ – kjetil b halvorsen May 19 '17 at 17:40
  • $\begingroup$ Have a look at researchgate.net/publication/… The plot is difficult to analyze only visually, in addition can you plot an autocorrelation function? It could be long time dependence, making it very difficult to assess stationarity from a short series you shown. Calculating Hurst exponents could be useful. $\endgroup$ – kjetil b halvorsen May 23 '17 at 10:34
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    $\begingroup$ Please merge your two accounts (account1 and account2) -- you can't edit from a different account than the one you posted from. $\endgroup$ – Glen_b May 23 '17 at 11:41
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This cannot be answered abstractly, we will need much more information. Relevant information needed to answer the question includes:

  • Frequency of observations. There might be yearly seasonality or 24-hour (daily, diurnal) cycles. If your data is means over 24-hour periods the last need not be considered.

  • Geographical location. Most places there would be a strong yearly cycle, but there might be exceptions to that.

Could you please augment your post with some plots, and the other auxiliary information?

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You should try with a stationarity test "Dickey-Fuller",

In statistics, the Dickey–Fuller test tests the null hypothesis of whether a unit root is present in an autoregressive model. The alternative hypothesis is different depending on which version of the test is used, but is usually stationarity or trend-stationarity.

There are several tools in python and R to solve this problem..

Also the "Augmented Dickey–Fuller test" is a more robust test which is used to the same purpose.

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