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.

[1]  J. Stock,et al.  A Comparison of Direct and Iterated Multistep Ar Methods for Forecasting Macroeconomic Time Series , 2005 .

[2]  Andrew A. Weiss,et al.  Multi-step estimation and forecasting in dynamic models , 1991 .

[3]  P. Young,et al.  Time series analysis, forecasting and control , 1972, IEEE Transactions on Automatic Control.

[4]  J. Stock,et al.  Forecasting Using Principal Components From a Large Number of Predictors , 2002 .

[5]  I. Helland.  Partial Least Squares Regression , 2006 .

[6]  Guillaume Chevillon,et al.  Direct Multi-Step Estimation and Forecasting , 2006 .

[7]  M. Stone.  Continuum regression: Cross-validated sequentially constructed prediction embracing ordinary least s , 1990 .

[8]  Prasad A. Naik,et al.  Partial least squares estimator for single‐index models , 2000 .

[9]  Wynne W. Chin,et al.  Handbook of Partial Least Squares , 2010 .

[10]  P. Groenen,et al.  Macroeconomic forecasting with matched principal components , 2008 .

[11]  P. Garthwaite.  An Interpretation of Partial Least Squares , 1994 .

[12]  Shu-Ing Liu,et al.  Model selection for multiperiod forecasts , 1996 .

[13]  In-Bong Kang,et al.  Multi-period forecasting using different models for different horizons: an application to U.S. economic time series data , 2003 .

[14]  Jonathan D. Cryer,et al.  Time Series Analysis , 1986 .

[15]  Richard A. Davis,et al.  Introduction to time series and forecasting , 1998 .

[16]  Robert Lund,et al.  Periodic Time Series Models , 2005 .

[17]  G. C. Tiao,et al.  Robustness of maximum likelihood estimates for multi-step predictions: The exponential smoothing case , 1993 .

[18]  学 加納,et al.  Partial Least Squares Regression を用いた蒸留塔製品組成の推定制御 , 1998 .

[19]  Philip Hans Franses,et al.  Time Series Models for Business and Economic Forecasting , 1998 .

[20]  Michael P. Clements,et al.  On the limitations of comparing mean square forecast errors , 1993 .

[21]  I. Helland.  Partial least squares regression and statistical models , 1990 .

[22]  R. J. Bhansali,et al.  Asymptotically efficient autoregressive model selection for multistep prediction , 1996 .