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Testing for the Existence of a Generalized Wiener Process- the Case of Stock Prices

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Abstract
In this article, we present two nonparametric trispectrum based tests for testing the hypothesis that an observed time series was generated by what we call a generalized Wiener process (GWP). Assuming the existence of a Weiner process for asset rates of return is critical to the Black-Scholes model and its extension by Merton (BSM). The Hinich trispectrum-based test of linearity and the trispectrum extension of the Hinich-Rothman bispectrum test for time reversibility are used to test the validity of BSM. We apply the tests to a selection of high frequency NYSE and Australian (ASX) stocks.

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  • Melvin. J. Hinich & Phillip Wild & John Foster, 2010. "Testing for the Existence of a Generalized Wiener Process- the Case of Stock Prices," Discussion Papers Series 408, School of Economics, University of Queensland, Australia.
    • Handle: RePEc:qld:uq2004:408
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    File URL: https://economics.uq.edu.au/files/44732/408.pdf
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    1. Melvin J. Hinich & Douglas M. Patterson, 1992. "A New Diagnostic Test Of Model Inadequacy Which Uses The Martingale Difference Criterion," Journal of Time Series Analysis, Wiley Blackwell, vol. 13(3), pages 233-252, May.
    2. Savin, N.E., 1984. "Multiple hypothesis testing," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 14, pages 827-879, Elsevier.
    3. Barnett,William A. & Geweke,John & Shell,Karl (ed.), 1989. "Economic Complexity: Chaos, Sunspots, Bubbles, and Nonlinearity," Cambridge Books, Cambridge University Press, number 9780521355636, September.
    4. Andrew W. Lo, A. Craig MacKinlay, 1988. "Stock Market Prices do not Follow Random Walks: Evidence from a Simple Specification Test," The Review of Financial Studies, Society for Financial Studies, vol. 1(1), pages 41-66.
    5. 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.
    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. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-654, May-June.
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