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?
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?
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.