Bivariate time series data often show strong relationships between the two components, while both individual variables can be approximated by random walks in the short run and are obviously bounded in the long run. Three model classes are considered for a time-series model selection problem: stable vector autoregressions, cointegrated models, and globally stable threshold models. It is demonstrated how simulated decision maps help in classifying observed time series. The maps process the joint evidence of two test statistics: a canonical root and an LR
type specification statistic for threshold effects.