This paper investigates the weak-form efficiency hypothesis for the art market. We consider 15 art price indices namely: Contemporary, Drawings, France, Global index (Euro), Global index (USD), Modern art, Nineteenth century, Old Masters, Paintings, Photographies, Postwar, Prints, Sculptures, UK and US. We use quarterly data from 1998:1 to 2015: 1. We employ both standard and non-parametric single and joint variance ratio tests while accounting for small sample bias through the use of the wild bootstrapping. We show that the majority of the art markets are inefficient with the exception of the Old Masters that consistently prove efficient under both individual and joint variance ratio tests. To a lesser extent Contemporary, US and UK markets are also efficient. However, confronting the data with both linear and nonlinear long memory models as robustness check, we observe that Paints, Prints, Photographies, Nineteenth century, Modern Art, US, France and Drawings have unit roots and are therefore efficient. Others such as Post war Sculpture, and Contemporary have values of the fractional parameter d significantly different from 0 to 1 and they may be considered efficient as well in a number of cases. The US and Contemporary art markets appear to be efficient irrespective of the method used.