In this paper, we deal with autoregressive processes with random coefficients. We propose a least-squares estimator for the fourth-order moments of both the innovation and disturbance noises and state its consistency. The main theme of the paper is the development of bootstrap procedures for the autoregressive parameter. We show how to obtain approximative residuals for the process even though the standard method for autoregressive processes does not work in this context since one then would obtain convoluted residuals of the innovation and disturbance noises. These ideas lead to a modification of the classical residual bootstrap for autoregressive processes. The consistency of the bootstrap procedure is established. Further, the estimators proposed in the first part are used to form two wild bootstrap modifications. Finally, the performances of the three bootstrap procedures are explored by a simulation study and compared with each other.