COWLES FOUNDATION FOR RESEARCH IN
ECONOMICS Box 208281
COWLES FOUNDATION DISCUSSION PAPER NO. 1871 Series Estimation of Stochastic Processes: Peter C.B. Phillips and Zhipeng Liao September 2012 This paper overviews recent developments in series estimation of
stochastic processes and some of their applications in econometrics. Underlying this
approach is the idea that a stochastic process may under certain conditions be represented
in terms of a set of orthonormal basis functions, giving a series representation that
involves deterministic functions. Several applications of this series approximation method
are discussed. The first shows how a continuous function can be approximated by a linear
combination of Brownian motions (BMs), which is useful in the study of the spurious
regressions. The second application utilizes the series representation of BM to
investigate the effect of the presence of deterministic trends in a regression on
traditional unit-root tests. The third uses basis functions in the series approximation as
instrumental variables (IVs) to perform efficient estimation of the parameters in
cointegrated systems. The fourth application proposes alternative estimators of long-run
variances in some econometric models with dependent data, thereby providing
autocorrelation robust inference methods in these models. We review some work related to
these applications and some ongoing research involving series approximation methods. |
