Reduced Rank Regression Models in Economics and Finance

This chapter surveys the importance of reduced rank regression techniques (RRR) for modelling economic and ?nancial time series. We mainly focus on models that are capable to reproduce the presence of common dynamics among variables such as the serial correlation common feature and the multivariate autoregressive index models. Cointegration analysis, for which RRR plays a central role, is not discussed in this chapter as it deserves a speci?c treatment on its own. Instead, we show how to detect and model comovements in time series that are stationary or that have been stationarized after proper transformations. The motivations for the use of RRR in time series econometrics include dimension reductions which simplify complex dynamics and thus making interpretations easier, as well as pursuing e¢ ciency gains in both estimation and prediction. Via the ?nal equation representation, RRR also makes the nexus between multivariate time series and parsimonious marginal ARIMA models. The drawback of RRR, which is common to all the dimension reduction techniques, is that the underlying restrictions may be present or not in the data. We provide in this chapter a couple of empirical applications to illustrate concepts and methods.