This study examines the time series characteristics of residential electricity demand and its determinants in Korea and the short-run and long-run relationship among them. We employ unit root tests, cointegration, and error-correction models on annual time series for the period 1972--2019. The rapid development of Korea over this period provides clear evidence of the possibility of structural breaks. We find that residential electricity demand and its determinants are trend-stationary processes with a slope change, which implies that there is no need to invoke cointegration methods under the unit root assumption. We expect that the essential modeling strategy presented in this article will be widely applicable.