We propose a nested reduced-rank regression (NRRR) approach in fitting model with multivariate functional responses and predictors to achieve tailored dimension reduction facilitate interpretation visualization. Our is based on two-level low-rank structure imposed the surfaces. A global identifies small set of latent principal that drives underlying association. local then controls complexity s...

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 presence common dynamics among variables such as serial correlation feature multivariate autoregressive index models. Cointegration analysis, which RRR plays a central role, is not discussed in this it deserves s...

where A is an unknown p× n matrix of coefficients and E is an unobserved m× n random noise matrix with independent mean zero and variance σ. We want to find an estimate  such that ||Y −XÂ|| is small. If we use standard least square estimation directly to estimate A in (1.1) without adding any constraints, then it is just the same as regressing each response on the predictors separately. In thi...