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Alternative Estimators of Long-Range Dependence


  • Fernandez Viviana

    () (Pontificia Universidad Catolica de Chile)


In this article, we concentrate on various techniques to quantify long-range dependence: wavelets, Geweke and Porter-Hudak (GPH)'s semi-parametric method, the periodogram method, rescaled range analysis (R/S) and a modification of it aimed at accommodating for short memory, quasi maximum likelihood (QML), de-trended fluctuation analysis (DFA), Modified DFA (MDFA), and Centered Moving Average (CMA) analysis.Based on Monte Carlo experiments, we conclude that if the data generating process (DGP) is an AR(1), MA(1) or ARMA(1, 1) process, with moderate parameter values, the periodogram, GPH, QML, and modified R/S methods, followed by the DFA, MDFA, and CMA ones, perform reasonably well as regards with bias, although some of these techniques exhibit a non-negligible size distortion. Moreover, the QML, the periodogram, DFA, MDFA, and CMA methods overall provide with powerful and low-bias estimators, under alternative ARFIMA (p, d, q)-DGPs. The wavelet-based estimator in turn has high power, but it is noticeably upward (downward) biased when the autoregressive (moving-average) coefficient of the DGP is large.Our Monte Carlo experiments are complemented with an application to Dow Jones AIG Gold Sub-index data, by means of bootstrap re-sampling.

Suggested Citation

  • Fernandez Viviana, 2011. "Alternative Estimators of Long-Range Dependence," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-37, March.
  • Handle: RePEc:bpj:sndecm:v:15:y:2011:i:2:n:5

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    References listed on IDEAS

    1. Los, Cornelis A. & Yu, Bing, 2008. "Persistence characteristics of the Chinese stock markets," International Review of Financial Analysis, Elsevier, vol. 17(1), pages 64-82.
    2. Ané, Thierry & Ureche-Rangau, Loredana, 2008. "Does trading volume really explain stock returns volatility?," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 18(3), pages 216-235, July.
    3. Lo, Andrew W, 1991. "Long-Term Memory in Stock Market Prices," Econometrica, Econometric Society, vol. 59(5), pages 1279-1313, September.
    4. Connor Jeff & Rossiter Rosemary, 2005. "Wavelet Transforms and Commodity Prices," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 9(1), pages 1-22, March.
    5. Newey, Whitney & West, Kenneth, 2014. "A simple, positive semi-definite, heteroscedasticity and autocorrelation consistent covariance matrix," Applied Econometrics, Publishing House "SINERGIA PRESS", vol. 33(1), pages 125-132.
    6. Grau-Carles, Pilar, 2006. "Bootstrap testing for detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 360(1), pages 89-98.
    7. Mielniczuk, J. & Wojdyllo, P., 2007. "Estimation of Hurst exponent revisited," Computational Statistics & Data Analysis, Elsevier, vol. 51(9), pages 4510-4525, May.
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    Cited by:

    1. Almurad, Zainy M.H. & Delignières, Didier, 2016. "Evenly spacing in Detrended Fluctuation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 451(C), pages 63-69.
    2. Tiwari, Aviral Kumar & Kumar, Satish & Pathak, Rajesh & Roubaud, David, 2019. "Testing the oil price efficiency using various measures of long-range dependence," Energy Economics, Elsevier, vol. 84(C).
    3. Benjamin Rainer Auer, 2018. "Are standard asset pricing factors long-range dependent?," Journal of Economics and Finance, Springer;Academy of Economics and Finance, vol. 42(1), pages 66-88, January.

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