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We consider the problem of maximum likelihood estimation of the parameter in the first-order autoregressive stationary process after loss of information due to hard limiting. For this particular transformation, the exact maximum likelihood estimator is found, and its distribution function is approximated. A numerical comparison with the common estimate obtained from the original data shows that, for moderate sample sizes and small variance of the error term, very little precision is lost as a result of the binary transformation. On the other hand, the suggested estimator is simple and easy to compute.