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A sequential procedure for testing the existence of a random walk model in finite samples


  • George Halkos
  • Ilias Kevork


Given the random walk model, we show, for the traditional unrestricted regression used in testing stationarity, that no matter what the initial value of the random walk is or its drift or its error standard deviation, the sampling distributions of certain statistics remain unchanged. Using Monte Carlo simulations, we estimate, for different finite samples, the sampling distributions of these statistics. After smoothing the percentiles of the empirical sampling distributions, we come up with a new set of critical values for testing the existence of a random walk, if each statistic is being used on an individual base. Combining the new sets of critical values, we finally suggest a general methodology for testing for a random walk model.

Suggested Citation

  • George Halkos & Ilias Kevork, 2008. "A sequential procedure for testing the existence of a random walk model in finite samples," Journal of Applied Statistics, Taylor & Francis Journals, vol. 35(8), pages 909-925.
  • Handle: RePEc:taf:japsta:v:35:y:2008:i:8:p:909-925 DOI: 10.1080/02664760802185290

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    References listed on IDEAS

    1. Nelson, Daniel B, 1991. "Conditional Heteroskedasticity in Asset Returns: A New Approach," Econometrica, Econometric Society, vol. 59(2), pages 347-370, March.
    2. Chung-Ming Kuan, 2006. "Artificial Neural Networks," IEAS Working Paper : academic research 06-A010, Institute of Economics, Academia Sinica, Taipei, Taiwan.
    3. Potter, Simon M, 1995. "A Nonlinear Approach to US GNP," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 10(2), pages 109-125, April-Jun.
    4. Ludlow, Jorge & Enders, Walter, 2000. "Estimating non-linear ARMA models using Fourier coefficients," International Journal of Forecasting, Elsevier, vol. 16(3), pages 333-347.
    5. Pami Dua & Nishita Raje & Satyananda Sahoo, 2004. "Interest Rate Modeling and Forecasting in India," Occasional papers 3, Centre for Development Economics, Delhi School of Economics.
    6. Engle, Robert F & Ng, Victor K, 1993. " Measuring and Testing the Impact of News on Volatility," Journal of Finance, American Finance Association, vol. 48(5), pages 1749-1778, December.
    7. Rabemananjara, R & Zakoian, J M, 1993. "Threshold Arch Models and Asymmetries in Volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(1), pages 31-49, Jan.-Marc.
    8. Engle, Robert F & Lilien, David M & Robins, Russell P, 1987. "Estimating Time Varying Risk Premia in the Term Structure: The Arch-M Model," Econometrica, Econometric Society, vol. 55(2), pages 391-407, March.
    9. Guy Melard, 1985. "Examples of the evolutionary spectrum theory," ULB Institutional Repository 2013/13696, ULB -- Universite Libre de Bruxelles.
    10. Swanson, Norman R & White, Halbert, 1995. "A Model-Selection Approach to Assessing the Information in the Term Structure Using Linear Models and Artificial Neural Networks," Journal of Business & Economic Statistics, American Statistical Association, vol. 13(3), pages 265-275, July.
    11. 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.
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    random walk; critical values; uncertainty;


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