A unifying view on multi-step forecasting using an autoregression

This paper unifies two methodologies for multi-step forecasting from autoregressive time series models. The first is covered in most of the traditional time series literature and it uses short-horizon forecasts to compute longer-horizon forecasts, while the estimation method minimizes one-step-ahead forecast errors. The second methodology considers direct multi-step estimation and forecasting. In this paper, we show that both approaches are special (boundary) cases of a technique called partial least squares (PLS) when this technique is applied to an autoregression. We outline this methodology and show how it unifies the other two. We also illustrate the practical relevance of the resultant PLS autoregression for 17 quarterly, seasonally adjusted, industrial production series. Our main findings are that both boundary models can be improved by including factors indicated from the PLS technique.

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