EM for a missing observation in a Gaussian AR1 process

In the expectation-maximization algorithm for a stationary autoregressive process of order one, a single missing interior value has a normal distribution conditional on its neighbors. The E-step uses both its conditional mean and its conditional second moment, not just mean imputation. The M-step maximizes the expected stationary complete-data log-likelihood, including the initial-observation density and the conditional-variance contribution to the two adjacent innovation squares.