We evaluate the asymptotic and finite-sample properties of direct multi-step estimation (DMS) for forecasting at several horizons. For forecast accuracy gains from DMS in finite samples, mis-specification and non-stationarity of the DGP are necessary, but when a model is well-specified, iterating the one-step ahead forecasts may not be asymptotically preferable. If a model is mis-specified for a non-stationary DGP, in particular omitting either negative residual serial correlation or regime shifts, DMS can forecast more accurately. Monte Carlo simulations clarify the non-linear dependence of the estimation and forecast biases on the parameters of the DGP, and explain existing results.

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This paper surveys the literature on multi-step forecasting when the model or the estimation method focuses directly on the link between the forecast origin and the horizon of interest. Among diverse contributions, we show how the current consensual concepts have emerged. We present an exhaustive overview of the existing results, including a conclusive review of the circumstances favourable to direct multi-step forecasting, namely different forms of non-stationarity and appropriate model design. We also provide a unifying framework which allows us to analyse the sources of forecast errors and hence of accuracy improvements from direct over iterated multi-step forecasting.