Search arXiv⌕ Search
Home/Archive/arXiv

arXiv · 2003.08787

A comparison of Hurst exponent estimators in long-range dependent curve time series

Han Lin Shang
View original source ↗Read source document ↗Export metadata ↓

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 models, we compare finite-sample bias, variance and mean square error among some time- and frequency-domain Hurst exponent estimators and make our recommendations.

Explore related subjects

math.STstat.APstat.TH

Keep this discovery

Explore connections, maps & timelines

BibTeXRIS

Han Lin Shang. 2020-03-17. A comparison of Hurst exponent estimators in long-range dependent curve time series. https://doi.org/10.1515/jtse-2019-0009

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Harmonic Entropy Estimator: Minimax Optimality and Semiparametric Efficiency for Infinite Alphabets

Shannon entropy estimation for discrete distributions is a classical nonparametric problem whose statistical limits are well characterized under finite support. Whether minimax and efficiency guarantees extend to infinite-support distributions remains open, in part because the expectation and variance of logarithm-transformed multinomial counts lack closed forms, forcing analyses to rely on bounding arguments rather than exact moment expressions. We address this obstacle with an algebraic framework built on an exact identity relating harmonic-transformed counts to their log-probabilities, yielding the harmonic entropy estimator. With this framework, we obtain two main results characterizing the statistical limits of this problem for distributions with sufficiently fast-decaying tails. First, for the class of distributions with at least quadratically decaying tails ($p_j \lesssim j^{-2}$), we establish that the $L_2$-minimax convergence rate is $1/n$, a rate anchored by estimator variance for both finite- and infinite-support distributions. Second, under the stronger condition $p_j = o(j^{-2})$, we demonstrate that the harmonic estimator is semiparametrically efficient: $\sqrt{n}[\hat{H}(\mathbf{X}_n) - H(X)]$ converges weakly to a normal distribution with variance achieving the semiparametric efficiency bound, $\mathrm{Var}[\log p(X)]$. Furthermore, the harmonic estimator is universally less biased than the plug-in estimator by circumventing the approximation error inherent to expectations of logarithm-transformed counts. More broadly, the harmonic approach may provide a foundation for developing new theory in entropy-based estimation, such as inference for mutual information under similar nonparametric regimes.

math.ST↗
arXiv2026

Dense alternating sign matrices and imprecise copulas

In this paper, we study discrete quasi-copulas and discrete imprecise copulas of minimal range, which naturally correspond to alternating sign matrices. We identify dense alternating sign matrices as a particularly well-behaved subclass. We prove that the associated discrete imprecise copulas are always coherent and hence avoid sure loss. We further show that a particular extension of the corresponding discrete quasi-copulas to the full domain preserves this structure and yields self-dual imprecise copulas. To the best of our knowledge, this provides the first general result in the literature showing how properties established for discrete imprecise copulas can be preserved when extending them to their full-domain counterpart. We conclude the paper by showing that, for general alternating sign matrices, the associated discrete imprecise copulas need not avoid sure loss, further emphasizing the special role of the subclass of dense alternating sign matrices. We establish, however, that the class of discrete quasi-copulas of minimal range is invariant under all defect transformations

math.ST↗
arXiv2026

How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?

We study the worst-case false discovery rate (FDR) of the Benjamini-Hochberg procedure for both one- and two-sided Gaussian tests with general correlation matrices. For each setting and given target FDR level $q$, we construct a family of finite Gaussian models whose FDR divided by $q$ diverges as $q\downarrow0$. This disproves any universal multiplicative FDR bound. Moreover, we establish new FDR lower bounds that are independent of the number of hypotheses. For two-sided tests, the worst-case FDR over the number of hypotheses, mean vector, and correlation matrix is at least an explicit ${\ell_{=}}(q)>q$: \[ \ell_{=}(q)=\frac{q\sqrt{\log(1/q)}}{2\sqrtπ}+c_\ell q+o(q), \qquad c_\ell=0.6492828\ldots. \] For one-sided tests, we show a lower bound $\ell_{\le}(q)>q$: \[ \ell_{\le}(q)=\frac{q\sqrt{\log(1/q)}}{\sqrtπ} +\frac q2+o(q). \] Finally, we prove the leading constants are sharp for a class of correlation matrices for both one- and two-sided tests.

math.ST↗