I need help for understanding how can I interpret this correlogram in order to determine the $p$, $d$ and $q$ orders for ARIMA model. I use Stata, and I am analysing a time series with really few data.
Since the PACF has more significant structure than the ACF the initially suggested model might be an MA model. The suggested order of the MA model would be 1 since there is only 1 significant ACF. For a longer/detailed discussion of model selection identification you might look at http://www.autobox.com/cms/index.php/blog/entry/build-or-make-your-own-arima-forecasting-model or basic model identification material from other available web sites . The important idea that untreated anomalies/deterministic structure can obfuscate the initial model identification. Over-modelling also known as kitchen-sink modelling such as a (3,0,3) frequently (read: nearly always) can creates/inject unreliable redundant ARIMA structure. If you post your data ( even a coded version) I will try and help specifically.
As I understand it, there is no objectively correct order, and the orders of ARMA/ARIMA you select may differ depending on which criterion you choose to optimise, e.g. whether you choose BIC or AIC, for instance. It is more an art than a science.
Given this, here is my 2c.
- The fact that the 1st lag ACF is negative and that the ACF dies out quickly suggests a low order of differencing is required. The order of differencing may even be zero, i.e. the series is stationary. This is easy to check using DF / Phillips Perron tests.
- The sharp cut-off of the ACF (notwithstanding point 8, which could be an anomaly) suggests the order of MA >0. Try three? The sharp cut off of the ACF also suggests a relatively low (<3) order for the AR part.
If it were me, what I would suggest is following the Box-Jenkins approach; - Using the intuition above, specify an ARIMA(3,0,3) (assuming stationarity). - Check for residual autocorrelation. - Assuming no residual autocorrelation, add and remove AR/MA lags iteratively in order to optimise your selection criterion. - Re-check your final model for residual serial correlation.