<p>This paper focuses on the estimation of autoregressive parameters in <i>k</i>-parallel first-order autoregressive models under the assumption that the model parameters may be homogeneous. Several estimation procedures are considered in the presence of uncertain prior information regarding the equality of these parameters. In particular, pooled, pretest, and James–Stein-type shrinkage estimators are proposed for estimating the vector of autoregressive coefficients and are compared with the unrestricted estimator. The asymptotic properties of the suggested estimators are derived analytically and evaluated in terms of their asymptotic distributional bias and quadratic risk. Monte Carlo simulation experiments are conducted to illustrate and support the theoretical findings. A real data application based on annual unemployment rates is also provided to demonstrate the practical performance of the proposed estimators.</p>