Multi-Step Forecasting in the Presence of Weak Trends

This paper studies the properties of processes which exhibit both a stochastic and a deterministic trend via local-asymptotics and introduces the concept of a 'weak' trend: both trends have the same order of magnitude and hence asymptotically interact. Resulting parameter estimators and forecast errors are functions of trending Ornstein-Uhlenbeck processes. In a comparison of direct and iterated multi-step estimation and forecasting of a potentially misspeci ed random walk with drift at various - fi xed or sample dependent - horizons, we derive, analytically and via simulation, the distributional properties of estimators and predictors at both short- and long-run horizons