We develop new semiparametric tests for double unit roots under a weakly dependent error structure of Phillips for tests for a unit root. The tests are based on symmetric estimation of Sen and Dickey. Through Monte Carlo simulations, the new tests are compared with the tests of Haldrup and of Dickey and Pantula. Our tests have empirical sizes close to the nominal size even when the innovations follow a negatively autocorrelated moving average, for which the semiparametric tests of Haldrup are oversized. Moreover, our tests have better power than the other two tests against I(1), explosive, and stationary alternatives. The tests are applied to the yearly Korean wholesale price and consumer price indexes. Some I(2) structure is evident for the indexes.