We consider nonstationary autoregressive autoregressive process with infinite variance of error. In the case of infinite cariance, the limiting distribution of the estimated coefficient is different from that under the finite cariance assumption. In this paper we show that the bootstrap method can be used to approximate the distribution of ordinary least squares estimator of the coefficient in the first order random walk process with infinite variance through some empirical studies and we suggest a test procedure based on bootstrap method for the unit root test.