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Convergence to Stochastic Integrals with Non-linear integrands

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Abstract

In this paper we present a general result concerning the convergence to stochastic integrals with non-linear integrands. The key finding represents a generalization of Chan and Wei's (1988) Theorem 2.4 and that of Ibragimov and Phillips' (2004) Theorem 8.2. This result is necessary for analysing the asymptotic properties of mis-specification tests, when applied to a unit root process, for which Wooldridge (1999) mentioned that the exiting results in the literature were not sufficient.

Suggested Citation

  • Bent Nielsen & Carlos Caceres, 2007. "Convergence to Stochastic Integrals with Non-linear integrands," Economics Papers 2007-W02, Economics Group, Nuffield College, University of Oxford.
  • Handle: RePEc:nuf:econwp:0702
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    File URL: http://www.nuffield.ox.ac.uk/economics/papers/2007/w2/Convergence_stochastic_integrals_2007_02_12.pdf
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    1. Ibragimov, Rustam & Phillips, Peter C.B., 2008. "Regression Asymptotics Using Martingale Convergence Methods," Econometric Theory, Cambridge University Press, vol. 24(4), pages 888-947, August.
    2. White, Halbert, 1980. "A Heteroskedasticity-Consistent Covariance Matrix Estimator and a Direct Test for Heteroskedasticity," Econometrica, Econometric Society, vol. 48(4), pages 817-838, May.
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    Cited by:

    1. Kuswanto, Heri & Sibbertsen, Philipp, 2009. "Testing for Long Memory Against ESTAR Nonlinearities," Hannover Economic Papers (HEP) dp-427, Leibniz Universit├Ąt Hannover, Wirtschaftswissenschaftliche Fakult├Ąt.

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    Keywords

    non-stationarity; unit roots; convergence; autoregressive processes; martingales stochastic integrals; non-linearity.;

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