The Limiting Behavior of the Estimated Parameters in a Misspecified Random Field Regression Model

Christian M. Dahl, Qin Yu
2008 Social Science Research Network  
This paper examines the limiting properties of the estimated parameters in the random field regression model recently proposed by Hamilton (Econometrica, 2001). 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
more » ... ied 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.
doi:10.2139/ssrn.1262227 fatcat:5eognwbfgvalnl57x5f23yjxxe