According to literature, oil price shocks and volatility can have sector-specific impacts in the market While these studies include most asset groups, the dynamic relationship between the oil market and Real Estate Investment Trusts (REITs) has not been tested. This study examines the role of oil price shocks and volatility on six REIT categories: Residential, Hotel, Healthcare, Retail, Mortgage and Warehouse/Industrial REITs for the January 2005-December 2013 period. In addition, a new causality approach is proposed by augmenting the Toda-Yamamoto method with a Fourier approximation. This approach is capable of capturing gradual or smooth shifts and does not require a prior knowledge regarding the number, dates, and form of structural breaks. The so-called Fourier Toda-Yamamoto causality (mean spillover) test finds uni-directional causality running from oil prices to all REITs, except for the mortgage REITs. In the latter case, the causality is reversed. In addition, the relatively new and simple causality-in-variance test shows that there is bi-directional volatility transmission between the oil market and all REITs. Our results have important implications for REIT managers and investors. (C) 2016 Published by Elsevier B.V.