In this note, a Cramer-Rao bound for the mean squared error that can be achieved with nonlinear observations of a nonlinear pth order autoregressive (AR) process where both the process and observation noise covariances can be state dependent is presented. The major limitation is that the AR process must be driven by an additive white Gaussian noise process that has a full-rank covariance. A numerical example demonstrating the tightness of the bound for a particular problem is included.