The second- and third-order coherence functions ${g}^{(n)}(0)$ ($n=2$ and 3) of an exciton-polariton condensate are measured and compared to the theory. Contrary to an ideal photon laser, deviation from unity in the second- and third-order coherence functions is observed, thus showing a bunching effect, but not the characteristics of a standard thermal state with ${g}^{(n)}(0)=n!$. The increase in bunching with the order of the coherence function, ${g}^{(3)}(0)>{g}^{(2)}(0)>1$, indicates that the polariton condensate is different from a coherent state, a number state, or a thermal state. The measurement of third-order coherence has the advantage, compared to the second-order one, that the difference between a thermal state and a coherent state is more pronounced. The experimental results are in agreement with the theoretical model where polariton-polariton and polariton-phonon interactions are responsible for the loss of temporal coherence.