seminar participants at the Bank of Finland for useful comments; Teppo Tammisto and Riccardo Verona for IT support; and Gregory Moore for editorial assistance. The views expressed are those of the authors and do not necessarily reect those of the Bank of Finland. Faria gratefully acknowledges nancial support from Fundação para a Ciência e Tecnologia through project UID/GES/00731/2016. AbstractWe generalize the Ferreira and Santa-Clara (2011) sum-of-the-parts method for forecasting stock market returns. Rather than summing the parts of stock returns, we suggest summing some of the frequency-decomposed parts. The proposed method signicantly improves upon the original sum-of-the-parts and delivers statistically and economically gains over historical mean forecasts, with monthly out-of-sample R 2 of 2.60 % and annual utility gains of 558 basis points. The strong performance of this method comes from its ability to isolate the frequencies of the parts with the highest predictive power, and from the fact that the selected frequency-decomposed parts carry complementary information that captures dierent frequencies of stock market returns.

Despite an increase in research -motivated by the global financial crisis of 2007-08 -empirical studies on the financial cycle are rare compared to those on the business cycle. This paper adds some new evidence to this scarce literature by using a different empirical methodology -wavelet analysis -to extract financial cycles from the data. Our results confirm that the U.S. financial cycle is (much) longer than the business cycle, but we do not find strong evidence supporting the view that the financial cycle has lengthened during the Great Moderation period.

Motivated by the U.S. events of the 2000s, we address whether a too low for too long interest rate policy may generate a boom-bust cycle. We simulate anticipated and unanticipated monetary policies in state-of-the-art DSGE models and in a model with bond nancing via a shadow banking system, in which the bond spread is calibrated for normal and optimistic times. Our results suggest that the U.S. boom-bust was caused by the combination of (i) too low for too long interest rates, (ii) excessive optimism and (iii) a failure of agents to anticipate the extent of the abnormally favorable conditions. Keywords: DSGE model, shadow banking system, too low for too long, boom-bust JEL codes: E32, E44, E52, G24 * This is a revised version of a paper that circulated previously under the title Monetary policy shocks in a DSGE model with a shadow banking system. We thank three anonymous referees and the Editor Carl E. Walsh, as well as Ricardo Reis, Michael Woodford, José Jorge and seminar participants at the University of Porto and Columbia University, for useful comments and suggestions. Verona is grateful to the Fundação para a Ciência e Tecnologia for nancial support (Ph.D. scholarship) and the Cournot Centre (Postdoctoral fellowship). The views expressed in this paper are those of the authors and should not be attributed to the European Commission nor to the Bank of Finland.