Discriminant analysis for dynamics of stable processes

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• 作者：Motoyoshi Nishikawa ; Masanobu Taniguchi
• 关键词：Stable process ; Spectral density ; Normalized power transfer functions ; Discriminant analysis ; Classification statistics
• 刊名：Statistical Methodology
• 出版年：2009
• 出版时间：January 2009
• 年：2009
• 卷：6
• 期：1
• 页码：82-96
• 全文大小：985 K

文摘

We consider the problem of classifying an α-stable linear process into two categories described by two hypotheses π₁ and π₂. These hypotheses are specified by the “normalized power transfer functions” and under π₁ and π₂, respectively. In this paper, we suggest a classification statistic based on the normalized power transfer functions. We show that is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as the sample size tends to infinity. When is contiguous to , we also evaluate the goodness of fit of in terms of the misclassification probabilities. Our results have potential applications in various fields, e.g., credit rating in finance, and so on. Several numerical examples will be given.