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.

中文翻译：

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远程相依曲线时间序列中Hurst指数估计的比较

摘要Hurst指数是自相似的远程依赖随机过程的最简单的数值总结。我们考虑在长期依赖曲线时间序列中对赫斯特指数的估计。我们的估算方法从构造长期协方差函数的估算开始，我们通过动态功能主成分分析将其用于估算跨越功能时间序列的主要子空间的正交函数。在功能自回归分数积分移动平均值（ARFIMA）模型的背景下，我们比较了一些时域和频域Hurst指数估计量之间的有限样本偏差，方差和均方误差，并提出了建议。