Nonparametric estimation in a nonlinear cointegration type model - Hans Arnfinn Karlsen; Terje Myklebust; Dag Tjøstheim (Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes, 2000)
We derive an asymptotic theory of nonparametric estimation for an nonlinear transfer function model Z(t) = f (Xt) + Wt where Xt and Zt are observed nonstationary processes and Wt is a stationary process. IN econometrics this can be interpreted as a nonlinear cointegration type relationship, but we believe that our results have wider interest. The class of nonstationary processes allowed for Xt is a subclass of the class of null recurrent.. Markov chains. This subclass contains the random walk model and the unit root processes. WE derive the asymptotics of an nonparametric estimate of f(z) under two alternative sets of assumptions on Wt: i) Wt is a linear process ii) Wt is a Markov chain satisfying some mixing conditions. The latter requires considerably more work but also holds larger promise for further developments. The finite sample properties f(x) are studied via a set of simulation experiments.
urn:nbn:de:kobv:11-10047396
Keywords: 330; cointegration; nonstationary time series models; null recurrent Markov chain; nonparametric kernel estimators; transfer function model