Gradual change-point is an important topic in statistical studies. However, due to the complexity of gradual change-points, they are more difficult than other types of change-points and have scarcely been discussed in the literature. Thus, we highlight that, at an unknown time, a continuous type of change in an autocorrelated coefficient exists. Using Bayesian and maximum likelihood estimation methods, we tested the existence of trends in an autoregressive coefficient with a linear change. Simulation results, which support the Bayesian estimation method and compare it with the maximum likelihood estimation method, are reported for illustration.