IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/41872.html

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
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/41872/1/MPRA_paper_41872.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/41879/1/MPRA_paper_41879.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. M. B. Priestley, 1980. "State‐Dependent Models: A General Approach To Non‐Linear Time Series Analysis," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 47-71, January.
    2. 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.
    3. Whitney Newey & Kenneth West, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 33(1), pages 125-132.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Franses,Philip Hans & Dijk,Dick van, 2000. "Non-Linear Time Series Models in Empirical Finance," Cambridge Books, Cambridge University Press, number 9780521770415, November.
    2. LeBaron, Blake, 2003. "Non-Linear Time Series Models in Empirical Finance,: Philip Hans Franses and Dick van Dijk, Cambridge University Press, Cambridge, 2000, 296 pp., Paperback, ISBN 0-521-77965-0, $33, [UK pound]22.95, [euro;]36.18, Hardback, ISBN 0-521-770416-0, $90, [," International Journal of Forecasting, Elsevier, vol. 19(4), pages 751-752.
    3. Franses,Philip Hans & Dijk,Dick van & Opschoor,Anne, 2014. "Time Series Models for Business and Economic Forecasting," Cambridge Books, Cambridge University Press, number 9780521817707, January.
    4. Pelletier, Denis, 2006. "Regime switching for dynamic correlations," Journal of Econometrics, Elsevier, vol. 131(1-2), pages 445-473.
    5. Korkmaz, Turhan & Cevik, Emrah Ismail & Gurkan, Serhan, 2010. "Testing the international capital asset pricing model with Markov switching model in emerging markets," MPRA Paper 71481, University Library of Munich, Germany, revised 2010.
    6. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    7. Robert J Bianchi & Adam E Clements & Michael E Drew, 2009. "HACking at Non-linearity: Evidence from Stocks and Bonds," School of Economics and Finance Discussion Papers and Working Papers Series 244, School of Economics and Finance, Queensland University of Technology.
    8. Peter C.B. Phillips & Mico Loretan, 1990. "Testing Covariance Stationarity Under Moment Condition Failure with an Application to Common Stock Returns," Cowles Foundation Discussion Papers 947, Cowles Foundation for Research in Economics, Yale University.
    9. Guy Melard, 1994. "Modèles linéaires et non linéaires," ULB Institutional Repository 2013/13804, ULB -- Universite Libre de Bruxelles.
    10. Jon Danielsson & Marcela Valenzuela & Ilknur Zer, 2023. "The Impact of Risk Cycles on Business Cycles: A Historical View," The Review of Financial Studies, Society for Financial Studies, vol. 36(7), pages 2922-2961.
    11. Bekaert, Geert & Engstrom, Eric & Ermolov, Andrey, 2015. "Bad environments, good environments: A non-Gaussian asymmetric volatility model," Journal of Econometrics, Elsevier, vol. 186(1), pages 258-275.
    12. Hui, Yongchang & Wong, Wing-Keung & Bai, Zhidong & Zhu, Zhenzhen, 2016. "A New Nonlinearity Test to Circumvent the Limitation of Volterra Expansion with Applications," MPRA Paper 75216, University Library of Munich, Germany.
    13. Panos K. Pouliasis & Christos Bentsos, 2024. "Oil price uncertainty and the relation to tanker shipping," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 2472-2494, April.
    14. Phillip Wild & John Foster, 2012. "On testing for non-linear and time irreversible probabilistic structure in high frequency ASX financial time series data," Discussion Papers Series 466, School of Economics, University of Queensland, Australia.
    15. Francq, Christian & ZakoI¨an, Jean-Michel, 2008. "Deriving the autocovariances of powers of Markov-switching GARCH models, with applications to statistical inference," Computational Statistics & Data Analysis, Elsevier, vol. 52(6), pages 3027-3046, February.
    16. Brock, W.A. & Dechert, W.D. & LeBaron, B. & Scheinkman, J.A., 1995. "A Test for Independence Based on the Correlation Dimension," Working papers 9520, Wisconsin Madison - Social Systems.
    17. Yacouba Boubacar Maïnassara & Landy Rabehasaina, 2020. "Estimation of weak ARMA models with regime changes," Statistical Inference for Stochastic Processes, Springer, vol. 23(1), pages 1-52, April.
    18. Ignacio Olmeda & Joaquin Pérez, 1995. "Non-linear dynamics and chaos in the Spanish stock market," Investigaciones Economicas, Fundación SEPI, vol. 19(2), pages 217-248, May.
    19. Zheng, Yao, 2015. "The linkage between aggregate investor sentiment and metal futures returns: A nonlinear approach," The Quarterly Review of Economics and Finance, Elsevier, vol. 58(C), pages 128-142.
    20. Richard D. F. Harris & Murat Mazibas, 2022. "A component Markov regime‐switching autoregressive conditional range model," Bulletin of Economic Research, Wiley Blackwell, vol. 74(2), pages 650-683, April.

    More about this item

    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:41872. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.