The limiting behavior of the estimated parameters in a misspecified random field regression model

Publikation: Working paperForskning

  • Christian Møller Dahl, Danmark
  • Yu Qin, Countrywide Financial Corporation, USA
  • Institut for Økonomi
This paper examines the limiting properties of the estimated parameters in
the random field regression model recently proposed by Hamilton (Econometrica,
2001). Though the model is parametric, it enjoys the flexibility of the nonparametric
approach since it can approximate a large collection of nonlinear functions and it
has the added advantage that there is no "curse of dimensionality."Contrary to
existing literature on the asymptotic properties of the estimated parameters in
random field models our results do not require that the explanatory variables are
sampled on a grid. However, as a consequence the random field model specification
introduces non-stationarity and non-ergodicity in the misspecified model and it
becomes non-trivial, relative to the existing literature, to establish the limiting
behavior of the estimated parameters. The asymptotic results are obtained by
applying some convenient new uniform convergence results that we propose. This
theory may have applications beyond those presented here. Our results indicate that
classical statistical inference techniques, in general, works very well for random field
regression models in finite samples and that these models succesfully can fit and
uncover many types of nonlinear structures in data.
UdgiverInstitut for Økonomi, Aarhus Universitet
Antal sider41
StatusUdgivet - 2008

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