# Interpreting a SARIMA model in SPSS - when is the model “good” enough for Interrupted Time Series

I am trying to analyse time trend data across a 10 year period (monthly) using SPSS, to do an interrupted time series analysis. I am not sure however, when a seasonal ARIMA model is "good enough". For example, I am using the Stationary R-squared as a guide, because the data is seasonal, and the highest I can get for one data series is 0.702 (3,0,0) x (1,2,1)12 The goodness of fit line with observed values is OK, but wondering when I should stop? Is it a bad thing if d in the seasonal component is 2? The SPSS expert modeller (ARIMA only seasonal box ticked) comes up with something completely different and a low stationary R-squared at 0.420 but the goodness of fit line seem to reflect the observed data better.

Is it also possible to conduct a seasonal decomposition and then use the seasonal adjusted data in a simple ARIMA model instead?

Any guidance would be appreciated, I seem to be going round in circles!

Thank you.

• $R^2$ is not the best indicator to use when selecting among a number of candidate models. More complicated models will normally give a higher $R^2$, but that does not mean that given the limited amount of data you will be able to estimate the more complicated models reliably. There is a tradeoff between how rich your model is and how well you are able to estimate it given the available data; in other words, a bias-variance tradeoff. You could look at AIC or BIC values instead (the model with the lower AIC or BIC value is preferred over a model with a higher value). – Richard Hardy Jun 9 '15 at 17:22
• That might explain why the "expert modeller" comes up with something different than you (it would surprise me if the "expert modeller" would just pick the model with the highest $R^2$ without realizing the problem of overfitting). It should in principle be possible to do the seasonal decomposition first and then use the seasonally-adjusted data for further ARIMA modelling. – Richard Hardy Jun 9 '15 at 17:23