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Comparing the Bias and Misspecification in Arfima Models

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  • Smith, Jeremy
  • Taylor, Nick
  • Yadav, Sanjay

Abstract

A number of papers have looked at the bias in the fractional integration parameter, d using a variety of alternative estimation techniques. This paper supplements that literature by investigating the bias in both the short-term and long-term parameters for a range of ARFIMA models using a more comprehensive range of estimation techniques. The results suggest that all estimation procedures yield slightly biased estimates of the long-run parameter, and that these biases become larger with the introduction of short-term AR or MA parameters. The bias in the short-run parameters mirrors that in the long-run parameters. These biases often causes model selection criteria to select an incorrect ARMA specification, having filtered out the long-run parameter. Incorrect specification of the short-run parameters in the ARFIMA model can accentuate the bias in the long-run parameter.

Suggested Citation

  • Smith, Jeremy & Taylor, Nick & Yadav, Sanjay, 1995. "Comparing the Bias and Misspecification in Arfima Models," The Warwick Economics Research Paper Series (TWERPS) 442, University of Warwick, Department of Economics.
    • Handle: RePEc:wrk:warwec:442
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    Cited by:

    1. Miguel Arranz & Francesc Marmol, 2001. "Out-of-sample forecast errors in misspecific perturbed long memory processes," Statistical Papers, Springer, vol. 42(4), pages 423-436, October.
    2. Giorgio Canarella & Stephen M Miller, 2017. "Inflation Persistence Before and After Inflation Targeting: A Fractional Integration Approach," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 43(1), pages 78-103, January.
    3. Leonardo Rocha Souza, 2007. "Temporal Aggregation and Bandwidth selection in estimating long memory," Journal of Time Series Analysis, Wiley Blackwell, vol. 28(5), pages 701-722, September.
    4. Ana Pérez & Esther Ruiz, 2002. "Modelos de memoria larga para series económicas y financieras," Investigaciones Economicas, Fundación SEPI, vol. 26(3), pages 395-445, September.
    5. Gadea, Maria Dolores & Sabate, Marcela & Serrano, Jose Maria, 2004. "Structural breaks and their trace in the memory: Inflation rate series in the long-run," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 14(2), pages 117-134, April.
    6. Giorgio Canarella & Stephen M. Miller, 2016. "Inflation Persistence and Structural Breaks: The Experience of Inflation Targeting Countries and the US," Working papers 2016-21, University of Connecticut, Department of Economics.
    7. Guglielmo Caporale & Luis Gil-Alana, 2013. "Long memory in US real output per capita," Empirical Economics, Springer, vol. 44(2), pages 591-611, April.
    8. Souza, Leonardo R. & Smith, Jeremy, 2004. "Effects of temporal aggregation on estimates and forecasts of fractionally integrated processes: a Monte-Carlo study," International Journal of Forecasting, Elsevier, vol. 20(3), pages 487-502.
    9. Onali, Enrico & Goddard, John, 2011. "Are European equity markets efficient? New evidence from fractal analysis," International Review of Financial Analysis, Elsevier, vol. 20(2), pages 59-67, April.
    10. Benjamin J. C. Kim & David Karemera, 2006. "Assessing the forecasting accuracy of alternative nominal exchange rate models: the case of long memory," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(5), pages 369-380.
    11. Shuping Shi & Jun Yu, 2023. "Volatility Puzzle: Long Memory or Antipersistency," Management Science, INFORMS, vol. 69(7), pages 3861-3883, July.
    12. Pong, Shiuyan & Shackleton, Mark B. & Taylor, Stephen J. & Xu, Xinzhong, 2004. "Forecasting currency volatility: A comparison of implied volatilities and AR(FI)MA models," Journal of Banking & Finance, Elsevier, vol. 28(10), pages 2541-2563, October.
    13. Fantazzini, Dean, 2023. "Assessing the Credit Risk of Crypto-Assets Using Daily Range Volatility Models," MPRA Paper 117141, University Library of Munich, Germany.
    14. Goddard, John & Onali, Enrico, 2012. "Short and long memory in stock returns data," Economics Letters, Elsevier, vol. 117(1), pages 253-255.
    15. Rea, William & Oxley, Les & Reale, Marco & Brown, Jennifer, 2013. "Not all estimators are born equal: The empirical properties of some estimators of long memory," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 93(C), pages 29-42.
    16. Leonardo Souza & Jeremy Smith & Reinaldo Souza, 2006. "Convex combinations of long memory estimates from different sampling rates," Computational Statistics, Springer, vol. 21(3), pages 399-413, December.
    17. Silva, E.M. & Franco, G.C. & Reisen, V.A. & Cruz, F.R.B., 2006. "Local bootstrap approaches for fractional differential parameter estimation in ARFIMA models," Computational Statistics & Data Analysis, Elsevier, vol. 51(2), pages 1002-1011, November.
    18. Beran, Jan & Ghosh, Sucharita & Schell, Dieter, 2009. "On least squares estimation for long-memory lattice processes," Journal of Multivariate Analysis, Elsevier, vol. 100(10), pages 2178-2194, November.
    19. Steven Clark & T. Coggin, 2011. "Are U.S. stock prices mean reverting? Some new tests using fractional integration models with overlapping data and structural breaks," Empirical Economics, Springer, vol. 40(2), pages 373-391, April.

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