Due to a variety of reasons, the Greek economy faced a severe crisis being a member of EMU. Nonetheless, the country's banking system experienced a dramatic outflow of deposits, in the period 2009–2015. The present paper attempts to shed light on the possibility of forecasting bank deposits, based on the keyword “Grexit” of Google searches. In this context, apart from standard forecasting models like AR (p) and ARDL (p, q) we estimate a novel Neural Network ARDL (p, q, G) model and its respective Bayesian modification. We show that extending standard autoregressive models with the information provided by Internet Searches leads to significant improvement in the forecasting accuracy of the Bank Deposits, compared with other standard models. Furthermore, the forecasting performance of the models, which are extended with Google searches, is shown to be better than models containing only the well-known indicators. Our findings are robust and econometrically sound.