Multiple Regression with Integrated Time Series

Recent work on the theory of regression with integrated process is reviewed. This work is particularly relevant in economics where many financial series and macroeconomic time series exhibit nonstationary characteristics and are often well modeled individually as simple ARIMA processes. The theory makes extensive use of weak convergence methods and allows for integrated processes that are driven by quite general weakly dependent and possibly heterogeneously distributed innovations. The theory also includes near integrated time series, which have roots near unity, and cointegrated series, which move together over time but are individually nonstationary. A general framework for asymptotic analysis is given which involves limiting Gaussian functionals and extends the LAN and LAMN families of conventional asymptotic theory. An application to the Gaussian AR(1) is reported.