COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1769 Semiparametric Estimation in Time Series of Simultaneous Equations Jiti Gao and Peter C. B. Phillips September 2010 A system of vector semiparametric nonlinear time series models is
studied with possible dependence structures and nonstationarities in the parametric and
nonparametric components. The parametric regressors may be endogenous while the
nonparametric regressors are strictly exogenous and represent trends. The parametric
regressors may be stationary or nonstationary and the nonparametric regressors are
nonstationary time series. This framework allows for the nonparametric treatment of
stochastic trends and subsumes many practical cases. Semiparametric least squares (SLS)
estimation is considered and its asymptotic properties are derived. Due to endogeneity in
the parametric regressors, SLS is generally inconsistent for the parametric component and
a semiparametric instrumental variable least squares (SIVLS) method is proposed instead.
Under certain regularity conditions, the SIVLS estimator of the parametric component is
shown to be consistent with a limiting normal distribution that is amenable to inference.
The rate of convergence in the parametric component is the usual vn rate and is explained
by the fact that the common (nonlinear) trend in the system is eliminated
nonparametrically by stochastic detrending. |
