We estimate three different models of speculative behaviour using oil price data. There are two major results: (i) The three-regime model of Brooks and Katsaris (2005) and a three-regime variant of van Norden and Schaller (2002) fit the oil price data reasonably well; and (ii) Both models show that the probabilities of being in a bubble collapsing state and a bubble expansion state spike in late-2008/early-2009. This provides some support for the claim by Phillips and Yu (2010) and Gilbert (2010) that a bubble in oil prices existed for short period in 2008.