Tourism is one of the most important industries of the Greek economy and is a key to economic growth. In 2019, 27.53 million tourists arrived in hotel and camping accommodations of the country. While these arrivals help the economic growth of the country, there is a need to meet the expectations of tourists in the context of the provided services. The tourism industry should make investments in the infrastructure of the destinations in order to accommodate and manage the tourist flows. These investments include transportation services, logistics, accommodation and health services. Therefore, different methods have used tourism industry data to come up with accurate forecasts of tourist arrivals. The research on tourism demand supports decision making bodies to develop and improve practices that contribute to tourism development. The main aim of the paper is to provide time series forecasting models of tourist arrivals in Greece in order to assist decision making bodies and stakeholders to develop and improve practices that contribute to tourism development. Moreover, this paper aims to contribute to the research field of tourism demand forecasting with a case study that concerns Greece. Historical data of tourist arrivals to the Ionian Islands, obtained from ELSTAT for the time period 2010-2018, have been used in the time series forecasting models used in this research.