On the use of pls regression for forecasting large sets of cointegrated time series

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.