Spurious Principal Components

The Principal Component Regression is often used to forecast macroeconomic variables when there are many predictors. In this letter, we argue that it makes sense to pre-whiten the predictors before including these in a PCR. With simulation experiments, we show that without such pre-whitening, spurious principal components can appear, and that these can become spuriously significant in a PCR. With an illustration to annual inflation rates for five African countries, we show that non-spurious principal components can be genuinely relevant in empirical forecasting models.