Climacogram versus autocovariance and power spectrum in stochastic modelling for Markovian and Hurst–Kolmogorov processes

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• 作者：Panayiotis Dimitriadis…
• 关键词：Stochastic modelling ; Climacogram ; Autocovariance ; Power spectrum ; Uncertainty ; Bias ; Turbulence
• 刊名：Stochastic Environmental Research and Risk Assessment (SERRA)
• 出版年：2015
• 出版时间：August 2015
• 年：2015
• 卷：29
• 期：6
• 页码：1649-1669
• 全文大小：12,567 KB
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• 作者单位：Panayiotis Dimitriadis (1)
  Demetris Koutsoyiannis (1)
  
  1. Department of Water Resources and Environmental Engineering, School of Civil Engineering, National Technical University of Athens, Heroon Polytechneiou 5, 158 80, Zographou, Greece
  
• 刊物类别：Earth and Environmental Science
• 刊物主题：Environment
  Mathematical Applications in Environmental Science
  Mathematical Applications in Geosciences
  Probability Theory and Stochastic Processes
  Statistics for Engineering, Physics, Computer Science, Chemistry and Geosciences
  Numerical and Computational Methods in Engineering
  Waste Water Technology, Water Pollution Control, Water Management and Aquatic Pollution
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1436-3259

文摘

Three common stochastic tools, the climacogram i.e. variance of the time averaged process over averaging time scale, the autocovariance function and the power spectrum are compared to each other to assess each one’s advantages and disadvantages in stochastic modelling and statistical inference. Although in theory, all three are equivalent to each other (transformations one another expressing second order stochastic properties), in practical application their ability to characterize a geophysical process and their utility as statistical estimators may vary. In the analysis both Markovian and non Markovian stochastic processes, which have exponential and power-type autocovariances, respectively, are used. It is shown that, due to high bias in autocovariance estimation, as well as effects of process discretization and finite sample size, the power spectrum is also prone to bias and discretization errors as well as high uncertainty, which may misrepresent the process behaviour (e.g. Hurst phenomenon) if not taken into account. Moreover, it is shown that the classical climacogram estimator has small error as well as an expected value always positive, well-behaved and close to its mode (most probable value), all of which are important advantages in stochastic model building. In contrast, the power spectrum and the autocovariance do not have some of these properties. Therefore, when building a stochastic model, it seems beneficial to start from the climacogram, rather than the power spectrum or the autocovariance. The results are illustrated by a real world application based on the analysis of a long time series of high-frequency turbulent flow measurements.