LTB universes as alternatives to dark energy: does positive averaged   acceleration imply positive cosmic acceleration?
  We show that positive averaged acceleration obtained in LTB models through spatial averaging can require integration over a region beyond the event horizon of the central observer. We provide an example of a LTB model with positive averaged acceleration in which the luminosity distance does not contain information about the entire spatially averaged region, making the averaged acceleration unobservable. Since the cosmic acceleration is obtained from fitting the observed luminosity distance to a FRW model we conclude that in general a positive averaged acceleration in LTB models does not imply a positive FRW cosmic acceleration. 
Antonio Enea Romano