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Testing for Equality of an Increasing Number of Spectral Density Functions

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Topics in Nonparametric Statistics

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 74))

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Abstract

Nowadays it is very frequent that a practitioner faces the problem of modelling large data sets. Some relevant examples include spatio-temporal or panel data models with large N and T. In these cases deciding a particular dynamic model for each individual/population, which plays a crucial role in prediction and inferences, can be a very onerous and complex task. The aim of this paper is thus to examine a nonparametric test for the equality of the linear dynamic models as the number of individuals increases without bound. The test has two main features: (a) there is no need to choose any bandwidth parameter and (b) the asymptotic distribution of the test is a normal random variable.

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References

  1. Brillinger, D.R.: Time series, Data Analysis and Theory. Holden-Day, San Francisco (1980)

    Google Scholar 

  2. Brillinger, D.R.: Time Series, Data Analysis and Theory. Holden-Day, San Francisco (1981)

    MATH  Google Scholar 

  3. Brockwell, P.J., Davis, R.A.: Time Series: Theory and Methods. Springer, New York (1991)

    Google Scholar 

  4. Brockwell, P.J., Davis, R.A.: Time series: Theory and Methods. Springer, New York (2000)

    Google Scholar 

  5. Chang, C., Ogden, R.T.: Bootstrapping sums of independent but not identically distributed continuous processes with applications to functional data. J. Multivariate Anal. 100, 1291–1303 (2009)

    Article  MATH  MathSciNet  Google Scholar 

  6. Coates, D.S., Diggle, P.J.: Test for computing two estimated spectral densities. J. Time Ser. Anal. 7, 7–20 (1986)

    Article  MATH  MathSciNet  Google Scholar 

  7. Degras, D., Xu, Z., Zhang, T., Wu, W.B.: Testing parallelism between trends in multiple time series. IEEE Trans. Signal Process. 60, 1087–1097 (2012)

    Article  MathSciNet  Google Scholar 

  8. Detter, H., Paparoditis, E.: Bootstrapping frequency domain tests in multivariate time series with an application to testing equality of spectral densities. J. Roy. Stat. Soc. Ser. B 71, 831–857 (2009)

    Article  Google Scholar 

  9. Diggle, P.J., Fisher, N.I.: Nonparametric comparison of cumulative periodograms. Appl. Stat. 40, 423–434 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  10. Ferraty, F., Vieu, P.: Nonparametric Functional Data Analysis: Theory and Practice. Springer, Berlin (2006)

    Google Scholar 

  11. Fuentes, M.: Testing for separability of spatial–temporal covariance functions. J. Stat. Plan. Inference 136, 447–466 (2006)

    Article  MATH  MathSciNet  Google Scholar 

  12. Grenander, U., Rosenblatt, M.: Statistical Analysis of Stationary Time Series. Wiley, New York (1957)

    MATH  Google Scholar 

  13. Hannan, E.J.: Multiple Time Series. Wiley, New York (1970)

    Book  MATH  Google Scholar 

  14. Härdle, W., Marron, T.S.: Semiparametric comparison of regression curves. Ann. Stat. 18, 63–89 (1990)

    Article  MATH  Google Scholar 

  15. Phillips, P.C.B., Moon, R.: Linear regression limit theory for nonstationary panel data. Econometrica 67, 1057–1111 (1999)

    Article  MATH  MathSciNet  Google Scholar 

  16. Pinkse, J., Robinson, P.M.: Pooling nonparametric estimates of regression functions with a similar shape. In: Maddala, G.S., Phillips, P.C.B., Srinivisan, T.N. (eds.) Statistical Methods in Econometrics and Quantitative Economics: A Volume in Honour of C.R. Rao, pp. 172–197. Wiley, Cambridge (1995)

    Google Scholar 

  17. Whittle, P.: On stationary processes in the plane. Biometrika 41, 434–449 (1954)

    Article  MATH  MathSciNet  Google Scholar 

  18. Zhang, Y., Su, L., Phillips, P.C.B.: Testing for common trends in semi-parametric panel data models with fixed effects. Econometrics J. 15, 56–100 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  19. Zhu, J., Lahiri, S.N., Cressie, N.: Asymptotic inference for spatial CDFS over time. Statistica Sinica 12, 843–861 (2002)

    MATH  MathSciNet  Google Scholar 

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Acknowledgements

Javier Hidalgo gratefully acknowledges the research support by a Catedra of Excellence by the Bank of Santander.

We are very grateful to the comments of a referee which have led to a much improve version of the paper. Of course, all the usual caveats are in placed for any remaining errors in the manuscript.

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Authors and Affiliations

  1. London School of Economics, London, UK

    Javier Hidalgo & Pedro C. L. Souza

Authors
  1. Javier Hidalgo
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  2. Pedro C. L. Souza
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Corresponding author

Correspondence to Javier Hidalgo .

Editor information

Editors and Affiliations

  1. Department of Statistics, The Pennsylvania State University, University Park, Pennsylvania, USA

    Michael G. Akritas

  2. Department of Statistics, North Carolina State University, Raleigh, North Carolina, USA

    S. N. Lahiri

  3. Department of Mathematics, University of California, San Diego, California, USA

    Dimitris N. Politis

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Hidalgo, J., Souza, P.C.L. (2014). Testing for Equality of an Increasing Number of Spectral Density Functions. In: Akritas, M., Lahiri, S., Politis, D. (eds) Topics in Nonparametric Statistics. Springer Proceedings in Mathematics & Statistics, vol 74. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-0569-0_13

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