Empirical evidence suggests that a large proportion of immigrants who initially intended to stay temporarily in the destination country end up staying permanently, which may lead to suboptimal integration. We study systematic causes of unexpected staying that originate in migrant misperceptions. Our framework contains uncertainty about long-term wages, endogenous integration and savings in the short term, and return migration in the long term. We identify necessary and sufficient conditions on misperceptions that lead migrants to overestimate their probability of return migration, independently of their characteristics. We show that these conditions involve pessimism about the destination country, either in terms of short-term utility, of long-term utility, or of wage prospects. We then highlight specific behavioural biases that give rise to such forms of pessimism. Using the German Socio-Economic Panel, we find that relatively higher pessimism at arrival about future utility and wages is associated with migrants staying unexpectedly ex post.