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New Non-Linearity Test to Circumvent the Limitation of Volterra Expansion

Author

Listed:
  • Bai, Zhidong
  • Hui, Yongchang
  • Wong, Wing-Keung

Abstract

In this article we propose a quick, efficient, and easy method to detect whether a time series Yt possesses any nonlinear feature. The advantage of our proposed nonlinearity test is that it is not required to know the exact nonlinear features and the detailed nonlinear forms of Yt. Our proposed test could also be used to test whether the model, including linear and nonlinear, hypothesized to be used for the variable is appropriate as long as the residuals of the model being used could be estimated. Our simulation results show that our proposed test is stable and powerful while our illustration on Wolf's sunspots numbers is consistent with the findings from existing literature.

Suggested Citation

  • Bai, Zhidong & Hui, Yongchang & Wong, Wing-Keung, 2012. "New Non-Linearity Test to Circumvent the Limitation of Volterra Expansion," MPRA Paper 41872, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:41872
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    File URL: https://mpra.ub.uni-muenchen.de/41879/1/MPRA_paper_41879.pdf
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    References listed on IDEAS

    as
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    2. Hamilton, James D, 1989. "A New Approach to the Economic Analysis of Nonstationary Time Series and the Business Cycle," Econometrica, Econometric Society, vol. 57(2), pages 357-384, March.
    3. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    4. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    5. Wolfgang Härdle & Helmut Lütkepohl & Rong Chen, 1997. "A Review of Nonparametric Time Series Analysis," International Statistical Review, International Statistical Institute, vol. 65(1), pages 49-72, April.
    6. Hinich, Melvin J & Patterson, Douglas M, 1985. "Evidence of Nonlinearity in Daily Stock Returns," Journal of Business & Economic Statistics, American Statistical Association, vol. 3(1), pages 69-77, January.
    7. Melvin J. Hinich, 1982. "Testing For Gaussianity And Linearity Of A Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 3(3), pages 169-176, May.
    8. T. Subba Rao & M. M. Gabr, 1980. "A Test For Linearity Of Stationary Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(2), pages 145-158, March.
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    Citations

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    Cited by:

    1. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," JRFM, MDPI, vol. 11(1), pages 1-29, March.
    2. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Decision Sciences, Economics, Finance, Business, Computing, And Big Data: Connections," Advances in Decision Sciences, Asia University, Taiwan, vol. 22(1), pages 36-94, December.
    3. Chang, C-L. & McAleer, M.J. & Wong, W.-K., 2018. "Decision Sciences, Economics, Finance, Business, Computing, and Big Data: Connections," Econometric Institute Research Papers 18-024/III, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    4. Chia-Lin Chang & Michael McAleer & Wing-Keung Wong, 2018. "Big Data, Computational Science, Economics, Finance, Marketing, Management, and Psychology: Connections," Journal of Risk and Financial Management, MDPI, Open Access Journal, vol. 11(1), pages 1-29, March.

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    More about this item

    Keywords

    linearity; nonlinearity; U-statistics; Volterra expansion;
    All these keywords.

    JEL classification:

    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • C01 - Mathematical and Quantitative Methods - - General - - - Econometrics

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