Abstract
Multi-step forecast is an important issue in time series analysis. Among linear forecasts, the direct and recursive methods are both popular in use. The former is solved by minimizing the h-step-ahead prediction mean squared error directly. The latter, also called plug-in or iterated method, is recursively computing the multi-step-ahead prediction by repeatedly plug in the one-step-ahead best linear predictors to unobserved lag variables. Both methods are theoretically justified, while their empirical performance relative to the other is depending on the tradeoff between the bias and estimation variance which is typically sensitive to the working model, the forecast horizon, and the underlying data scenario. This thesis proposes a composite inference for parameter estimation as well as for the multi-step forecasting by combining the estimating functions from both direct and recursive methods. This new composite method is easy to compute and is expected to remain the advantages from both sides. In particular, the new method can automatically adjust the optimal weights between both predictors via a cross validation approach. Simulation studies show that the proposed composite forecast performs effectively and adaptive towards the better one among the traditional direct and recursive forecasts under a variety of linear and nonlinear data generating scenarios. Some practical recommendations and computational issues are also addressed.