Reduced Rank Regression Models in Economics and Finance

Reduced rank regression (RRR) has been extensively employed for modelling economic and financial time series. The main goals of RRR are to specify and estimate models that are capable of reproducing the presence of common dynamics among variables such as the serial correlation common feature and the multivariate autoregressive index models. Although cointegration analysis is likely the most prominent example of the use of RRR in econometrics, a large body of research is aimed at detecting and modelling co-movements 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 make interpretations easier, as well as the pursuit of efficiency gains in both estimation and prediction. Via the final equation representation, RRR also makes the nexus between multivariate time series and parsimonious marginal ARIMA (autoregressive integrated moving average) models. RRR’s drawback, which is common to all of the dimension reduction techniques, is that the underlying restrictions may or may not be present in the data.