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Spurious Regressions with Stationary Gegenbauer Processes and Harmonic Processes


  • Sun, Yixiao


This paper studies the spurious regressions among stationary Gegenbauer processes, stationary harmonic processes and deterministic trigonometric series. We find the spurious regression can occur between two stationary Gegenbauer processes, as long as their generalized fractional differencing parameters sum up to a value greater than 0.5 and their spectral densities have poles at the same location. The spurious regression may also be present between a stationary Gegenbauer process and a stationary harmonic process, or between a stationary Gegenbauer process and a deterministic trigonometric series, as long as the poles of the discreet Fourier transforms or the spectral densities of underlying processes are located at the same frequency. Our findings suggest that it is the strong persistence and cyclical comovement that cause the spurious effect. Our theoretical results are supported by simulations.

Suggested Citation

  • Sun, Yixiao, 2003. "Spurious Regressions with Stationary Gegenbauer Processes and Harmonic Processes," University of California at San Diego, Economics Working Paper Series qt1g23v6p5, Department of Economics, UC San Diego.
  • Handle: RePEc:cdl:ucsdec:qt1g23v6p5

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    References listed on IDEAS

    1. Hwang, Soosung & Satchell, Stephen E, 1999. "Modelling Emerging Market Risk Premia Using Higher Moments," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 4(4), pages 271-296, October.
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    3. Bates, David S, 1996. "Jumps and Stochastic Volatility: Exchange Rate Processes Implicit in Deutsche Mark Options," Review of Financial Studies, Society for Financial Studies, vol. 9(1), pages 69-107.
    4. Campbell R. Harvey & Akhtar Siddique, 2000. "Conditional Skewness in Asset Pricing Tests," Journal of Finance, American Finance Association, vol. 55(3), pages 1263-1295, June.
    5. Philippe Jorion, 1988. "On Jump Processes in the Foreign Exchange and Stock Markets," Review of Financial Studies, Society for Financial Studies, vol. 1(4), pages 427-445.
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    Cited by:

    1. Sun, Yixiao, 2006. "Spurious regressions between stationary generalized long memory processes," Economics Letters, Elsevier, vol. 90(3), pages 446-454, March.


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