Regularly varying stochastic processes model extreme dependence betweenprocess values at different locations and/or time points. For such processes wepropose a two-step parameter estimation of the extremogram, when some part ofthe domain of interest is fixed and another increasing. We provide conditionsfor consistency and asymptotic normality of the empirical extremogram centredby a pre-asymptotic version for such observation schemes. For max-stableprocesses with Fr{'e}chet margins we provide conditions, such that theempirical extremogram (or a bias-corrected version) centred by its true versionis asymptotically normal. In a second step, for a parametric extremogram model,we fit the parameters by generalised least squares estimation and proveconsistency and asymptotic normality of the estimates. We propose subsamplingprocedures to obtain asymptotically correct confidence intervals. Finally, weapply our results to a variety of Brown-Resnick processes. A simulation studyshows that the procedure works well also for moderate sample sizes.
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机译：定期不同的随机过程模型在不同位置和/或时间点之间进行过程之间的极端依赖性。对于这样的过程，当利益领域的某些部分是固定的并且另一个增加的情况下，Wepropose的两步参数估计。我们为逐渐变量的偏振标题进行了一致性和渐近常态，为这种观察计划进行了渐近版的一致性和渐近常态。对于具有FR {'e} CHET MARGINS的MAX-stableProcess，我们提供条件，例如由其真正版本的渐近正常的偏离辐射信号（或偏置校正版本）。在第二步中，对于参数辐条正级别模型，我们通过概括最小二乘估计和估计的渐近性和渐近常态来符合参数。我们提出了分支过程，以获得渐近纠正的置信区间。最后，将我们的结果培养到各种棕色重新纳米进程。模拟轮廓，程序的运作良好也适用于适度的样本尺寸。
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