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Testing for Breaks in Regression Models with Dependent Data

  • J. HidalgoEmail author
  • V. Dalla
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 175)

Abstract

The paper examines a test for smoothness/breaks in a nonparametric regression model with dependent data. The test is based on the supremum of the difference between the one-sided kernel regression estimates. When the errors of the model exhibit strong dependence, we have that the normalization constants to obtain the asymptotic Gumbel distribution are data dependent and the critical values are difficult to obtain, if possible. This motivates, together with the fact that the rate of convergence to the Gumbel distribution is only logarithmic, the use of a bootstrap analogue of the test. We describe a valid bootstrap algorithm and show its asymptotic validity. It is interesting to remark that neither subsampling nor the sieve bootstrap will lead to asymptotic valid inferences in our scenario. Finally, we indicate how to perform a test for k breaks against the alternative of \(k+k_{0}\) breaks for some \(k_{0}\).

Keywords

Nonparametric regression Breaks/smoothness Strong dependence Extreme-values distribution Frequency domain bootstrap algorithms 

Notes

Acknowledgments

We like to thank Marie Huskova for their comments on a previous version of the paper. Of course, any remaining errors are our sole responsibility.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.London School of EconomicsLondonUK
  2. 2.National and Kapodistrian University of AthensAthensGreece

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