Higher time derivatives, stability and Fermi Statistics

We show that statistics is crucial for the instability problem derived from higher time derivatives. In fact, and contrary to previous statements, we check that when dealing with Fermi systems, the Hamiltonian is well bounded and the quantum states are normalizable. Although, ghost states are still present, they do not affect unitarity under certain conditions. We first analyze a quantum oscillator involving Grassman variables and then we generalize it to a Dirac field. Finally, we discuss some physical implications