Piecewise local linear estimation of functional equilibrium relationships

We introduce a new nonparametric approach for estimating a simple varying coeffcient model with a unit root nonstationarity. Our method is based on a piecewise local least squares principle and is computationally simple to implement. We establish its asymptotic properties and evaluate its performance in finite samples. Our working model also allows us to formalise the concept of a long run functional equilibrium relationship analogous to the well known cointegration concept within a constant coefficient setting