Long-term forecast on the size of future economy measured by real GDP is essential to planning and evaluation of long-term fiscal policy as well as pension reform and design of welfare system. The most widely used method for the forecast is production function approach which often depends upon noisy measurement of capital stock as well as ad-hoc assumptions for future productivity growth. In this paper, we avoid using them by fitting AR(1) model with non-linear deterministic trend. The problem of testing unit root while determining the order of trend polynomial at the same time is taken care of by applying sequential unit root test. We find that Korean real GDP data has quadratic deterministic trend instead of the often assumed stochastic trend. Iterative PW-GLS forecast shows that Korean GDP growth rate will fall to 2.35% in 2050 while it drops further to 0.66% when the effect of population ageing is incorporated.