摘要翻译：
我们考虑了由重尾持续时间引起的二阶长程相关过程。我们将这种现象称为持续时间驱动的长程依赖(DDLRD)，而不是更广泛研究的基于$IID$过程的分数差分的线性长程依赖。我们详细考虑了两个具有DDLRD的具体过程，最初在Taqqu和Levy(1986)和Parke(1999)中提出。对于这些过程，我们得到了适当标准化的离散傅里叶变换和样本自协方差的极限分布。在低频下，标准化的DFTs收敛到一个稳定的规律，标准化的样本自协方差在固定的滞后下也收敛到一个稳定的规律。在固定滞后集上，标准化样本自协方差的有限集合收敛于退化分布。标准化的DFTs在高频下收敛于高斯律。对于所研究的两个DDLRD过程，我们的渐近结果惊人地相似。我们用一个模拟研究来校准我们的渐近结果，并研究了记忆参数的半参数对数周期图回归估计的性质。
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英文标题：
《Asymptotics for Duration-Driven Long Range Dependent Processes》
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作者：
Meng-Chen Hsieh, Clifford M. Hurvich (IOMS), Philippe Soulier
  (MODAL'X)
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最新提交年份：
2007
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分类信息：

一级分类：Mathematics        数学
二级分类：Statistics Theory        统计理论
分类描述：Applied, computational and theoretical statistics: e.g. statistical inference, regression, time series, multivariate analysis, data analysis, Markov chain Monte Carlo, design of experiments, case studies
应用统计、计算统计和理论统计：例如统计推断、回归、时间序列、多元分析、数据分析、马尔可夫链蒙特卡罗、实验设计、案例研究
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一级分类：Statistics        统计学
二级分类：Statistics Theory        统计理论
分类描述：stat.TH is an alias for math.ST. Asymptotics, Bayesian Inference, Decision Theory, Estimation, Foundations, Inference, Testing.
Stat.Th是Math.St的别名。渐近，贝叶斯推论，决策理论，估计，基础，推论，检验。
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英文摘要：
  We consider processes with second order long range dependence resulting from heavy tailed durations. We refer to this phenomenon as duration-driven long range dependence (DDLRD), as opposed to the more widely studied linear long range dependence based on fractional differencing of an $iid$ process. We consider in detail two specific processes having DDLRD, originally presented in Taqqu and Levy (1986), and Parke (1999). For these processes, we obtain the limiting distribution of suitably standardized discrete Fourier transforms (DFTs) and sample autocovariances. At low frequencies, the standardized DFTs converge to a stable law, as do the standardized sample autocovariances at fixed lags. Finite collections of standardized sample autocovariances at a fixed set of lags converge to a degenerate distribution. The standardized DFTs at high frequencies converge to a Gaussian law. Our asymptotic results are strikingly similar for the two DDLRD processes studied. We calibrate our asymptotic results with a simulation study which also investigates the properties of the semiparametric log periodogram regression estimator of the memory parameter.
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PDF链接：
https://arxiv.org/pdf/705.2701