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• Multi-step ahead demand forecasting is an important and cutting-edge research topic. • An effective forecasting approach incorporating privileged information is proposed. • The new paradigm (termed learning using privileged information (LUPI)) is imployed. • LUPI can efficiently grasp and model nonlinear characteristics of tourism data. • The empirical results verify its superiority and robustness with different samples. Accurate tourism demand forecasting can provide effective guidance for government management and tourism planning. Specifically, multi-step ahead tourism demand forecasting is of great relevance in guiding managers to develop strategies and assisting operators in business planning and is therefore of great interest to researchers and practitioners. However, it is usually difficult to obtain satisfactory accuracy in views of sophisticated data characteristics. This study proposes an improved machine learning paradigm, introducing valuable additional information into the training phase, which is not available for forecasting in the testing phase. Taking Hawaii (Daily and Weekly) and Macau tourist arrivals as the samples, the empirical evidence indicates that the proposed approach can significantly enhance the multi-step ahead forecasting performance from the view of both error calculation and statistical test. In particular, the paradigm's robustness is also demonstrated in the comparison of sliding window predictions with models of variants. [ABSTRACT FROM AUTHOR]