Phillips, P. C. B.; Durlauf, S. N. Multiple time series regression with integrated processes. (English) Zbl 0599.62103 Rev. Econ. Stud. 53, 473-495 (1986). An invariance principle for multiple time series is formulated and proved as the starting point for investigation of integrated models. A multiple time series \(y_ t=Ay_{t-1}+u_ t\) is analyzed, where \(u_ t\) is a weakly stationary sequence. The authors develop an asymptotic theory for sample moments of this integrated process and construct a test of \(H_ 0: A=I\). Then they examine the multiple regression equation \(y_ t=Ax_ t+u_ t\), where \(x_ t=x_{t-1}+v_ t\). The elements of the matrix A are unknown parameters and \((u_ t,v_ t)\) are joint innovations. A test of \(H_ 0: R vec A=r\) is proposed, where R and r are known. Asymptotical properties of this test are quite different from those of classical regression tests. The results are extended to models with fitted drift vectors. The research is motivated by some evidence about the behaviour of macroeconomic time series. Reviewer: J.Anděl Cited in 1 ReviewCited in 179 Documents MSC: 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH) 60F17 Functional limit theorems; invariance principles 91B84 Economic time series analysis Keywords:ARIMA; vector autoregression; hypothesis testing; invariance principle; multiple time series; integrated process PDFBibTeX XMLCite \textit{P. C. B. Phillips} and \textit{S. N. Durlauf}, Rev. Econ. Stud. 53, 473--495 (1986; Zbl 0599.62103) Full Text: DOI Link