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

Author

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  • Christian M. Dahl
  • Yu Qin

    () (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

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.

Suggested Citation

  • Christian M. Dahl & Yu Qin, 2008. "The limiting behavior of the estimated parameters in a misspecified random field regression model," CREATES Research Papers 2008-45, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2008-45
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    File URL: ftp://ftp.econ.au.dk/creates/rp/08/rp08_45.pdf
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    Cited by:

    1. Bond Derek & Harrison Michael J. & O'Brien Edward J., 2005. "Investigating Nonlinearity: A Note on the Estimation of Hamilton's Random Field Regression Model," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(3), pages 1-43, September.
    2. repec:tcd:wpaper:tep4 is not listed on IDEAS

    More about this item

    Keywords

    Random fields regressions; Estimation; Inference; Asymptotics;

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics

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