Inference after model selection is a very important problem. Model selection algorithms for ARIMA time series, with criteria such as AIC and BIC, tend to select an inconsistent model with positive probability, making data-splitting inference for testing and confidence intervals unreliable. One technique was fairly reliable for sample sizes greater than 600, and a modification also worked. Model selection is often useful for prediction, since the selected submodel tends to have fitted values and residuals that are highly correlated with those of the full model. A few prediction intervals perform fairly well even after model selection. A useful technique for handling outliers is to replace the outliers with missing values.