Reduced rank models for multiple time series. (English) Zbl 0612.62121

Velu, Raja P.; Reinsel, Gregory C.; Wichern, Dean W.

Biometrika 73, 105-118 (1986).

By analogy with the multivariate reduced rank regression model: \(Y_ t=ABX_ t+\epsilon_ t\), where A and B are \(m\times r\) and \(r\times n\) matrices respectively, the authors investigate reduced rank models for multiple time series \[ Y_ t=A(L)B(L)Y_{t-1}+\epsilon_ t \] where L denotes the lag operator, A and B are \(m\times r\) and \(r\times n\) matrix polynomial operators of degrees \(p_ 2\) and \(p_ 1\) respectively. The estimation of parameters and associated asymptotic theory are derived. To illustrate the methods, US hog and corn data are considered.

Reviewer: I.G.Zhurbenko

MSC:

62M10

Time series, auto-correlation, regression, etc. in statistics (GARCH)

Keywords:

autoregressive processes; canonical analysis; reduced rank regression; reduced rank models; multiple time series; matrix polynomial operators; estimation of parameters; asymptotic theory