<p>The authors propose a new class of autoregressive conditional interval (ACI) models for interval-valued time series data. A minimum distance method is proposed to estimate the parameters of an ACI model, and the consistency, asymptotic normality and asymptotic efficiency of the proposed estimator are established. It is shown that a two-stage minimum distance estimator is asymptotically most efficient among a class of minimum distance estimators, and it achieves the Cramer-Rao lower bound when the left and right bounds of the interval innovation process follow a bivariate normal distribution. Simulation studies and empirical applications show that the two-stage minimum distance estimator outperforms conditional least squares estimators based on the ranges and/or midpoints of the interval sample, as well as the conditional quasi-maximum likelihood estimator based on the bivariate left and right bounds of the interval sample.</p>