A UNIFYING VIEW ON MULTI‐STEP FORECASTING USING AN AUTOREGRESSION
统一了两种多步预测方法，证明它们都是偏最小二乘法应用于自回归时的特例，并用17个工业生产序列展示了该方法的实际改进效果。
Abstract 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.