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For a country to efficiently monitor international migration, quick access to information on migration flows is helpful. However, traditional data sources fail to provide immediate information on migration flows and do not facilitate the correct anticipation of these flows in the short term. To tackle this issue, this paper evaluates the predictive capacity of big data to estimate the current level or to predict short-term flows. The results show that Google Trends can provide information that reflects the attractiveness of Switzerland for to immigrants from different countries and predict, to some extent, current and future (short-term) migration flows of adults arriving from Spain or Italy. However, the predictions appear not to be satisfactory for other flows (from France and Germany). Additional studies based on alternative approaches are needed to validate or overturn our study results.