Usual test of testing unit root tests such as Dickey-Fuller (DF), Augmented Dickey-Fuller (ADF), Phillips-Perron (PP) and Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) tests ignore sign and boundary parameters. Ignorance of these problems may results in unusual estimate and test results. This paper demonstrates the ignorance of sign and boundary of parameters and consequences in estimation and hypothesis test by Monte Carlo simulation. This work proposes a distance-based optimum solution for testing unit root subject to the restriction of boundary and sign problem. Monte Carlo simulation study shows that the proposed one-sided test of testing unit root performs better than the usual tests interms of power property.