Abstract
This paper proposes a methodology to forecast cointegrated time series using many predictors. In particular, we show that Partial Least Squares can be used to estimate single-equation models that take into account of possible long-run relations among the predicted variable and the predictors. Based on Helland (Scand. J. Stat. 17:97–114, 1990), and Helland and Almoy (J. Am. Stat. Assoc. 89:583–591, 1994), we discuss the conditions under which Partial Least Squares regression provides a consistent estimate of the conditional expected value of the predicted variable. Finally, we apply the proposed methodology to a well-known dataset of US macroeconomic time series (Stock and Watson, Am. Stat. Assoc. 97:1167–1179, 2005). The empirical findings suggest that the new method improves over existing approaches to data-rich forecasting, particularly when the forecasting horizon becomes larger.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Notes
- 1.
The replication files are available on the web page http://homepages.ulb.ac.be/dgiannon/.
References
Banbura M, Giannone D, Reichlin L (2010) Large bayesian vector auto regressions. Journal of Applied Econometrics 25:71–72.
Banerjee A, Marcellino M (2007) Factor augmented error correction models. In: Castle J, Shepard N (eds) The methodology and practice of econometrics: a festschrift for David Hendry, pp. 227–254, Oxford University Press, Oxford
Boivin J, Ng S (2006) Are more data always better for factor analysis? Journal of Econometrics 132:169–194
Cubadda G, Hecq A (2011) Testing for common autocorrelation in data rich environments, Journal of Forecasting 30:325–335. DOI: 10.1002/for.1186
De Mol C, Giannone D, Reichlin L (2008) Forecasting using a large number of predictors: is bayesian regression a valid alternative to principal components? Journal of Econometrics 146:318–328
Engle R, Granger C (1987) Co-integration and error correction: representation, estimation and testing. Econometrica 55:2:251–276
Forni M, Lippi M, Reichlin L (2004) The Generalized factor model: consistency and rates. Journal of Econometrics 119:231–255
Forni M, Lippi M, Reichlin L (2005) The generalized dynamic factor model: one-sided estimation and forecasting. Journal of the American Statistical Association 100:830–840
Gröen JJ, Kapetanios G (2008) Revisiting useful approaches to data-rich macroecnomic forecasting. Federal Reserve Bank of New York Staff Reports 327
Helland S (1990) Partial least squares regression and statistical models. Scandinavian Journal of Statistics 17:97–114
Helland S, Almoy T (1994) Comparison of prediction methods when only a few components are relevant. Journal of the American Statistical Association 89:583–591
Johansen S (1996) Likelihood-based inference in cointegrated vector autoregressive models. Oxford University Press, Oxford
Snell A, (1999) Testing for r versus r − 1 cointegrating vectors. Journal of Econometrics 88: 151–191
Stock JH, Watson MW (2002a) Forecasting using principal components from a large number of predictors. Journal of the American Statistical Association 97:1167–1179
Stock JH, Watson MW (2002b) Mocroeconomic forecasting using diffusion index. Journal of Business and Economics Statistics 20:147–162
Stock JH, Watson MW (2005) An empirical comparison of methods for forecasting using many predictors, Manuscript, Princeton University, Princeton
Wold H (1985) Partial least squares. In Kotz S, Johnson NL (eds) Encyclopedia of the Statistical Sciences 6:581–591. John Wiley & Sons, New York
Acknowledgements
We thank Alain Hecq as well as an anonymous referee for useful comments and corrections. The usual disclaimers apply.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2012 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Cubadda, G., Guardabascio, B. (2012). On the Use of PLS Regression for Forecasting Large Sets of Cointegrated Time Series. In: Di Ciaccio, A., Coli, M., Angulo Ibanez, J. (eds) Advanced Statistical Methods for the Analysis of Large Data-Sets. Studies in Theoretical and Applied Statistics(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-21037-2_16
Download citation
DOI: https://doi.org/10.1007/978-3-642-21037-2_16
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-21036-5
Online ISBN: 978-3-642-21037-2
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)