A sorted leading indicators dynamic (SLID) factor model for short-run euro-area GDP forecasting

This paper introduces a statistical model for short-term GDP forecasting based on approximate dynamic factors (Stock and Watson methodology), extracted from a very large number of leading indicators sorted according to their correlations at various lags to euro-area GDP (Sorted Leading Indicators Dynamic factor model). A very large data set of 2000 series covering a variety of leading indicators for all countries of the euro area and the euro area itself was built for the model in order to meet consistency requirements. All series are introduced at different lags, thus several times, in the data set in order to extract dynamic factors (stacked version of the Stock and Watson model). Factors estimation is further enhanced by data filtering: indicators which contain little information about the business cycle at a given lag are dropped from the data set at this lag. The criterion for the information content of the series is their cross-correlation to GDP. Finally, forecasts are not based on a regression using fitted factors, but on a more parsimonious framework: the recursive projection of GDP on the first few factors by descending order of eigenvalues (augmented EM algorithm), since it is assumed that only the first eigenvectors corresponding to the larger shares of the data variance should account for common shocks and provide consistent estimations of factors. There is a broad consensus that "true" (latent) factors can be consistently estimated with an approximate factor model provided that the cross-section dimension of the data is far greater than the number of observations. Our real-time out-of-sample experiment showed that it is indeed efficient for short-term forecasting to use a very large number of series and the same series introduced at various lags. The short-term forecast accuracy is nevertheless enhanced by data filtering, as it seems that an appropriate level of filtering removes subsets of series with very low correlation to the reference variable but high idiosyncratic cross-correlation that might bias factor estimation with an approximate factor model. We assume here that the greater the accuracy of factor-based forecasts is, the closer the estimated factors are to the "true true" factors. The optimal threshold of filtering was estimated empirically and seems data set specific.