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Nonlinear Time Series Modeling: A Unified Perspective, Algorithm and Application

Author

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  • Subhadeep Mukhopadhyay

    (Department of Statistical Science, Temple University, Philadelphia, PA 19122, USA)

  • Emanuel Parzen

    (Department of Statistics, Texas A&M University, College Station, TX 77843, USA
    Shortly after finishing the first draft of this paper, Manny Parzen passed away. Deceased 6 February 2016.)

Abstract

A new comprehensive approach to nonlinear time series analysis and modeling is developed in the present paper. We introduce novel data-specific mid-distribution-based Legendre Polynomial (LP)-like nonlinear transformations of the original time series { Y ( t ) } that enable us to adapt all the existing stationary linear Gaussian time series modeling strategies and make them applicable to non-Gaussian and nonlinear processes in a robust fashion. The emphasis of the present paper is on empirical time series modeling via the algorithm LPTime. We demonstrate the effectiveness of our theoretical framework using daily S&P 500 return data between 2 January 1963 and 31 December 2009. Our proposed LPTime algorithm systematically discovers all the ‘stylized facts’ of the financial time series automatically, all at once, which were previously noted by many researchers one at a time.

Suggested Citation

  • Subhadeep Mukhopadhyay & Emanuel Parzen, 2018. "Nonlinear Time Series Modeling: A Unified Perspective, Algorithm and Application," JRFM, MDPI, vol. 11(3), pages 1-17, July.
    • Handle: RePEc:gam:jjrfmx:v:11:y:2018:i:3:p:37-:d:156708
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    References listed on IDEAS

    as
    1. Granger, Clive W J, 1993. "Strategies for Modelling Nonlinear Time-Series Relationships," The Economic Record, The Economic Society of Australia, vol. 69(206), pages 233-238, September.
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    3. Robert F. Engle & Simone Manganelli, 2004. "CAViaR: Conditional Autoregressive Value at Risk by Regression Quantiles," Journal of Business & Economic Statistics, American Statistical Association, vol. 22, pages 367-381, October.
    4. Clive Granger & Jin‐Lung Lin, 1994. "Using The Mutual Information Coefficient To Identify Lags In Nonlinear Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(4), pages 371-384, July.
    5. David F. Hendry, 2011. "Empirical Economic Model Discovery and Theory Evaluation," Rationality, Markets and Morals, Frankfurt School Verlag, Frankfurt School of Finance & Management, vol. 2(46), October.
    6. 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.
    7. C. W. J. Granger & Roselyne Joyeux, 1980. "An Introduction To Long‐Memory Time Series Models And Fractional Differencing," Journal of Time Series Analysis, Wiley Blackwell, vol. 1(1), pages 15-29, January.
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    Cited by:

    1. Chia-Lin Chang, 2020. "Editorial for Applied Econometrics," JRFM, MDPI, vol. 13(9), pages 1-5, August.

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