2017/04/19 by Sven Buhl, Claudia Klüppelberg, Buhl, Sven +1
Decision Sciences · Economics, Econometrics and Finance · Mathematics · #37A25 #60F05 #60G70 #62F12 #62G32 #62M30 #62P12 #Advanced Statistical Process Monitoring #FOS: Mathematics #Financial Risk and Volatility Modeling #Monetary Policy and Economic Impact #Statistical Methods and Inference #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1704.05656
openalex publication_date 2017/04/19 · openalex created_date 2022/10/03 · openalex updated_date 2026/07/28
Regularly varying stochastic processes model extreme dependence between\nprocess values at different locations and/or time points. For such processes we\npropose a two-step parameter estimation of the extremogram, when some part of\nthe domain of interest is fixed and another increasing. We provide conditions\nfor consistency and asymptotic normality of the empirical extremogram centred\nby a pre-asymptotic version for such observation schemes. For max-stable\nprocesses with Fr 'echet margins we provide conditions, such that the\nempirical extremogram (or a bias-corrected version) centred by its true version\nis asymptotically normal. In a second step, for a parametric extremogram model,\nwe fit the parameters by generalised least squares estimation and prove\nconsistency and asymptotic normality of the estimates. We propose subsampling\nprocedures to obtain asymptotically correct confidence intervals. Finally, we\napply our results to a variety of Brown-Resnick processes. A simulation study\nshows that the procedure works well also for moderate sample sizes.\n