We propose the autoregressive HMM for speech synthesis. We show that the autoregressive HMM supports efficient EM parameter estimation and that we can use established effective synthesis techniques such as synthesis considering global variance with minimal modification. The autoregressive HMM uses the same model for parameter estimation and synthesis in a consistent way, in contrast to the standard HMM synthesis framework, and supports easy and efficient parameter estimation, in contrast to the trajectory HMM. We find that the autoregressive HMM gives performance comparable to the standard HMM synthesis framework on a Blizzard Challenge-style naturalness evaluation.