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A Comparison of Hurst Exponent Estimators in Long-range Dependent Curve Time Series

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  • Shang Han Lin

    (Australian National University, Research School of Finance, Actuarial Studies and Statistics, Level 4, Building 26C, Kingsley St, Acton, Canberra, Australian Capital Territory, 2601, Australia)

Abstract

The Hurst exponent is the simplest numerical summary of self-similar long-range dependent stochastic processes. We consider the estimation of Hurst exponent in long-range dependent curve time series. Our estimation method begins by constructing an estimate of the long-run covariance function, which we use, via dynamic functional principal component analysis, in estimating the orthonormal functions spanning the dominant sub-space of functional time series. Within the context of functional autoregressive fractionally integrated moving average (ARFIMA) models, we compare finite-sample bias, variance and mean square error among some time- and frequency-domain Hurst exponent estimators and make our recommendations.

Suggested Citation

  • Shang Han Lin, 2020. "A Comparison of Hurst Exponent Estimators in Long-range Dependent Curve Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 12(1), pages 1-39, January.
    • Handle: RePEc:bpj:jtsmet:v:12:y:2020:i:1:p:39:n:3
    DOI: 10.1515/jtse-2019-0009
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    1. Han Lin Shang, 2023. "Sieve bootstrapping the memory parameter in long-range dependent stationary functional time series," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 107(3), pages 421-441, September.

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