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  • Ioannis Kasparis (a1)

We examine the limit properties of the nonlinear least squares (NLS) estimator under functional form misspecification in regression models with a unit root. Our theoretical framework is the same as that of Park and Phillips (2001, Econometrica 69, 117–161). We show that the limit behavior of the NLS estimator is largely determined by the relative orders of magnitude of the true and fitted models. If the estimated model is of different order of magnitude than the true model, the estimator converges to boundary points. When the pseudo-true value is on a boundary, standard methods for obtaining rates of convergence and limit distribution results are not applicable. We provide convergence rates and limit theory when the pseudo-true value is an interior point. If functional form misspecification is committed in the presence of stochastic trends, the convergence rates can be slower and the limit distribution different than that obtained under correct specification.

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*Address correspondence to Ioannis Kasparis, Department of Economics, University of Cyprus, P.O. Box 20537, CY-1678 Nicosia, Cyprus; e-mail:
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Andrews D.W.K. (1999) Estimation when a parameter is on a boundary. Econometrica 67, 1341–383.
Bates D.M. & Watts D.G. (1988) Nonlinear Regression Analysis and Its Applications. Wiley.
Bierens H.J. (1984) Model specification testing of time series regressions. Journal of Econometrics 26, 323–353.
Bierens H.J. (1990) A consistent test of functional form. Econometrica 58, 1443–1458.
Cox D.R. (1961) Tests for separate families of hypotheses. Journal of the Royal Statistical Society, Series B 32, 323–344.
Cox D.R. (1962) Further results on tests of separate families of hypotheses. Journal of the Royal Statistical Society Series B 24, 406–424.
Davidson R. & McKinnon J.G. (1981) Several tests for model specification in the presence of alternative hypotheses. Econometrica 49, 781–793.
de Jong R.M. (2004) Addendum to “Asymptotics for nonlinear transformations of integrated time series.” Econometric Theory 20, 627–635.
de Jong R.M. & Hu L. (2006) Nonlinear Models with Integrated Regressors and Convergence Order Results. Working paper, Department of Economics, Ohio State University.
de Jong R.M. & Wang C.-H. (2002) Further results on the asymptotics for nonlinear transformations of integrated time series. Econometric Theory 21, 413–430.
Domowitz I. & White H. (1982) Misspecified models with dependent observations. Journal of Econometrics 20, 35–58.
Hamilton J.D. (1994) Time Series Analysis. Princeton University Press.
Hansen L.P. (1982) Large sample properties of generalized method of moments estimators. Econometrica 50, 1029–1054.
Jeganathan P. (2003) Second Order Limits of Functionals of Sums of Linear Processes That Converge to Fractional Stable Motions. Working paper, Indian Statistical Institute.
Jeganathan P. (2004) Limits of functionals of sums of linear processes that converge to fractional stable motions. Annals of Probability 32, 1771–1795.
Jennrich R.I. (1969) Asymptotic properties of non-linear least squares estimation. Annals of Mathematical Statistics 40, 633–643.
Kasparis I. (2008a) Detection of functional form misspecification in cointegrating relations. Econometric Theory 24, 1373–1403.
Kasparis I. (2008b) Functional Form Misspecification in Regressions with a Unit Root. Working paper 08-02, Department of Economics, University of Cyprus.
Newey W.K. & McFadden D.M. (1994) Large sample estimation and hypothesis testing. In Engle R.F. & McFadden D.L. (eds.), Handbook of Econometrics, vol. 4, pp. 2213–2145. Elsevier.
Park J.Y. & Phillips P.C.B. (1999) Asymptotics for nonlinear transformations of integrated time series. Econometric Theory 15, 269–298.
Park J.Y. & Phillips P.C.B. (2000) Nonstationary binary choice. Econometrica 68, 1249–1280.
Park J.Y. & Phillips P.C.B. (2001) Nonlinear regressions with integrated time series. Econometrica 69, 117–161.
Pötscher B.M. (2004) Nonlinear functions and convergence to Brownian motion: Beyond the continuous mapping theorem. Econometric Theory 20, 1–22.
Ramsey J.B. (1969) Classical model selection through specification error tests. Journal of the Royal Statistical Society, Series B 32, 350–371.
van der Vaart A.W. & Wellner J.A. (1996) Weak Convergence and Empirical Processes: With Applications in Statistics. Springer Series in Statistics. Springer-Verlag.
Vuong Q.H. (1989) Likelihood ratio tests for model selection and non-nested hypotheses. Econometrica 57, 307–333.
Wang Q. & Phillips P.C.B. (2009) Asymptotic theory for local time density estimation and nonparametric cointegrating regression. Econometric Theory 25, 710–738.
White H. (1981) Consequences and detection of misspecified nonlinear regression models. Journal of the American Statistical Association 76, 419–433.
White H. & Domowitz I. (1984) Nonlinear regression with dependent observations. Econometrica 52, 143–162.
Wooldridge J.M. (1994) Estimation and inference for dependent processes. In Eagle R.F. & McFadden D.L. (eds.) Handbook of Econometrics, vol. 4, pp. 2639–2738, Elsevier.
Wu C.F. (1981) Asymptotic theory for non-linear least squares estimation. Annals of Statistics 9, 501–513.
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Econometric Theory
  • ISSN: 0266-4666
  • EISSN: 1469-4360
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