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Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory

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  • Afonso Goncalves da Silva
  • Peter Robinson

Abstract

Nonlinear functions of multivariate financial time series can exhibit long memory and fractional cointegration. However, tools for analysing these phenomena have principally been justified under assumptions that are invalid in this setting. Determination of asymptotic theory under more plausible assumptions can be complicated and lengthy. We discuss these issues and present a Monte Carlo study, showing that asymptotic theory should not necessarily be expected to provide a good approximation to finite-sample behavior.

Suggested Citation

  • Afonso Goncalves da Silva & Peter Robinson, 2008. "Finite Sample Performance in Cointegration Analysis of Nonlinear Time Series with Long Memory," Econometric Reviews, Taylor & Francis Journals, vol. 27(1-3), pages 268-297.
    • Handle: RePEc:taf:emetrv:v:27:y:2008:i:1-3:p:268-297
    DOI: 10.1080/07474930701873382
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    1. Morten Ørregaard Nielsen, 2005. "Semiparametric Estimation in Time‐Series Regression with Long‐Range Dependence," Journal of Time Series Analysis, Wiley Blackwell, vol. 26(2), pages 279-304, March.
    2. Robinson, Peter M. & Yajima, Yoshihiro, 2002. "Determination of cointegrating rank in fractional systems," Journal of Econometrics, Elsevier, vol. 106(2), pages 217-241, February.
    3. Morten Ørregaard Nielsen & Per Houmann Frederiksen, 2005. "Finite Sample Comparison of Parametric, Semiparametric, and Wavelet Estimators of Fractional Integration," Econometric Reviews, Taylor & Francis Journals, vol. 24(4), pages 405-443.
    4. da Silva, Afonso Gonçalves & Robinson, Peter M., 2008. "Fractional Cointegration In Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1207-1253, October.
    5. Robinson, P.M. & Henry, M., 1999. "Long And Short Memory Conditional Heteroskedasticity In Estimating The Memory Parameter Of Levels," Econometric Theory, Cambridge University Press, vol. 15(3), pages 299-336, June.
    6. Javier Hualde & Peter Robinson, 2006. "Semiparametric Estimation of Fractional Cointegration," Faculty Working Papers 07/06, School of Economics and Business Administration, University of Navarra.
    7. Deo, Rohit S. & Hurvich, Clifford M., 2001. "On The Log Periodogram Regression Estimator Of The Memory Parameter In Long Memory Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 17(4), pages 686-710, August.
    8. Clifford M. Hurvich & Eric Moulines & Philippe Soulier, 2005. "Estimating Long Memory in Volatility," Econometrica, Econometric Society, vol. 73(4), pages 1283-1328, July.
    9. Marinucci, D & Robinson, Peter M., 2001. "Semiparametric fractional cointegration analysis," LSE Research Online Documents on Economics 2269, London School of Economics and Political Science, LSE Library.
    10. Clifford M. Hurvich & Rohit Deo & Julia Brodsky, 1998. "The mean squared error of Geweke and Porter‐Hudak's estimator of the memory parameter of a long‐memory time series," Journal of Time Series Analysis, Wiley Blackwell, vol. 19(1), pages 19-46, January.
    11. Chambers, Marcus J, 1998. "Long Memory and Aggregation in Macroeconomic Time Series," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 39(4), pages 1053-1072, November.
    12. Marinucci, D. & Robinson, P. M., 2001. "Semiparametric fractional cointegration analysis," Journal of Econometrics, Elsevier, vol. 105(1), pages 225-247, November.
    13. D Marinucci & Peter M Robinson, 2001. "Semiparametric Fractional Cointegration Analysis," STICERD - Econometrics Paper Series 420, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
    14. Clifford M. Hurvich & Bonnie K. Ray, 2003. "The Local Whittle Estimator of Long-Memory Stochastic Volatility," Journal of Financial Econometrics, Oxford University Press, vol. 1(3), pages 445-470.
    15. Christensen, Bent Jesper & Nielsen, Morten Orregaard, 2006. "Asymptotic normality of narrow-band least squares in the stationary fractional cointegration model and volatility forecasting," Journal of Econometrics, Elsevier, vol. 133(1), pages 343-371, July.
    16. Javier Hidalgo & Peter M. Robinson, 2002. "Adapting to Unknown Disturbance Autocorrelation in Regression with Long Memory," Econometrica, Econometric Society, vol. 70(4), pages 1545-1581, July.
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    Cited by:

    1. Marcel Aloy & Gilles de Truchis, 2012. "Estimation and Testing for Fractional Cointegration," Working Papers halshs-00793206, HAL.
    2. Dalla, Violetta, 2015. "Power transformations of absolute returns and long memory estimation," Journal of Empirical Finance, Elsevier, vol. 33(C), pages 1-18.

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    More about this item

    Keywords

    Fractional cointegration; Memory estimation; Stochastic volatility;
    All these 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

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