Abstract
In the literature, Li and Heckman (2003) considered forecasting by local linear extrapolation； however, it does not deal with correlated data. In addition, Gijbels, Pope and Wand (GPW) (1999) investigated some relationships between nonparametric regression and exponential moving average, but extrapolation was not considered. This thesis considers local linear extrapolation for correlated data and re-examines equivalence relationships between double exponential smoothing and nonparametric regression. We give explicit expressions that show the equivalence between double exponential smoothing and local linear regression. Further, we derive the asymptotic bias and variance from the perspectives of double exponential smoothing and the asymptotically optimal smoothing is calculated. Stimulation studies are conducted to examine prediction performance of local linear extrapolation and double exponential smoothing and to compare them with the estimator in GPW (1999). We also investigate selecting the smoothing factor and bandwidth by forward cross validation in stimulations. We find that when data has long-term trends, local linear extrapolation tends to have smaller mean square error than the other two approaches； when data exhibits sudden change of trends, the estimator by GPW performs better; and the double exponential smoothing has the best performance in the state-space model.