Publication Date: December 2019
This paper develops an asymptotic theory for nonlinear cointegrating power function regression. The framework extends earlier work on the deterministic trend case and allows for both endogeneity and heteroskedasticity, which makes the models and inferential methods relevant to many empirical economic and ﬁnancial applications, including predictive regression. Accompanying the asymptotic theory of nonlinear regression, the paper establishes some new results on weak convergence to stochastic integrals that go beyond the usual semi-martingale structure and considerably extend existing limit theory, complementing other recent ﬁndings on stochastic integral asymptotics. The paper also provides a general framework for extremum estimation limit theory that encompasses stochastically nonstationary time series and should be of wide applicability.
Keywords: Nonlinear power regression, Least squares estimation, Nonstationarity, Endogeneity, Heteroscedasticity
JEL Classification Codes: C13, C22