This paper studies the relationship between saving and investment rates in Greece using annual time series data for the period 1980-2012. The stationarity analysis is conducted by applying Zivot and Andrews unit root test while for cointegration we apply the ARDL bounds testing approach developed by Pesaran-Shin-Smith. Cointegration test show the presence of a long run relationship between the series that we examine in the presence of a structural variance. Therefore, the Feldstein–Horioka puzzle which is presented in the Greek open economy with a high rate of capital mobility during the 1980’s and 1990’s is not valid. The augmented Granger causality test shows that both in the short and long run there is a one direction causal relationship between savings and investment with direction from savings to investment. Finally, variance decompositions show that domestic savings are the main cause of investment in a long run basis.