Regression with integrated regressors

Abstract

The ordinary least-squares (OLS) estimation in regression models with integrated regressors is considered. The limiting distribution of the OLS estimator is established under suitable normalization. This unifies asymptotic results for various models studied by numerous authors in the past. It is shown that the limiting distribution of the OLS estimator in the polynomial regression and that in the unstable autoregression can be expressed by the same functional defined on the set of all continuous functions on [0, 1]. The functional evaluated at the standard Brownian motion gives the limiting distribution of the OLS estimator in the unstable autoregression. The functional evaluated at the identity function gives the limiting distribution of the OLS estimator in the polynomial regression model. Application of our theory is also illustrated in autoregression containing a polynomial trend and stable random components.