hey, I have a dataset that contains hourly wind speeds. When I plotted my original acf, it showed seasonality at every 24 lags so I applied a difference of 24 to remove seasonality and another difference to remove trends. The diagrams shows the resulting acf and pacf, how do I determine the order of the arima model. Also I am seeing that at every 24 lags in the pacf there is a spike and decaying slowly, is this suppose to happen or does my dataset still contains stationarity?
A good starting point can be the forecast package of prof Hyndman in R. The
auto.arima() function can give you a suitable model and this can be a good starting point of your investigation. I have learned a lot from his open book https://www.otexts.org/fpp/
In response to Pankaj Joshi (thanks for asking !): See Interrupted Time Series Analysis - ARIMAX for High Frequency Biological Data? where @AdamO correctly reflected/opined "The correlogram should be calculated from residuals using a model that controls for intervention administration, otherwise the intervention effects are taken to be Gaussian noise, underestimating the actual autoregressive effect.". This comment reflects the fact that if there are interventions present they effectively mask the true (but unknown) arima structure. Prof. J.K.Ord once commented to me that is is like the "Alice in Wonderland effect".
Interventions must be specified either by the user or detected by Intervention Detection procedures. The problem/opportunity is to simultaneously identify BOTH arima structure & the Interventions as is done by AUTOBOX, a piece of software that I have helped to develop.
Since auto.arima naively assumes no Intervention series and constant parameters over time and constant error variance over time it is easily confused and delivers inadequate results which is frequently cited in these pages .
Complete transparency suggests that I mention https://cran.r-project.org/web/packages/tsoutliers/index.html as a tool to identify interventions which requires the user to pre-specify the form of the ARIMA model and fails to consider time varying parameters and time varying error variance.
So the erroneously suggested "logic" goes .. use a two step approach STEP 1:... use auto.arima to identify the ARIMA portion assuming no interventions present in the data THEN in STEP 2 identify the interventions that were assumed not to be present in the first step. Patch the two answers together !
If you wish you can post your data and I will report the results of a simultaneous identification strategy where embedded interdependent heuristics are employed to simultaneously suggest a possibly useful answer.