TY - JOUR

T1 - Discriminant analysis for dynamics of stable processes

AU - Nishikawa, Motoyoshi

AU - Taniguchi, Masanobu

PY - 2009/1/1

Y1 - 2009/1/1

N2 - 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" over(f, ̃) (λ) and over(g, ̃) (λ) under π1 and π2, respectively. In this paper, we suggest a classification statistic In (over(f, ̃), over(g, ̃)) based on the normalized power transfer functions. We show that In (over(f, ̃), over(g, ̃)) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as the sample size tends to infinity. When over(g, ̃) (λ) is contiguous to over(f, ̃) (λ), we also evaluate the goodness of fit of In (over(f, ̃), over(g, ̃)) 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.

AB - 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" over(f, ̃) (λ) and over(g, ̃) (λ) under π1 and π2, respectively. In this paper, we suggest a classification statistic In (over(f, ̃), over(g, ̃)) based on the normalized power transfer functions. We show that In (over(f, ̃), over(g, ̃)) is a consistent classification criterion in the sense that the misclassification probabilities converge to zero as the sample size tends to infinity. When over(g, ̃) (λ) is contiguous to over(f, ̃) (λ), we also evaluate the goodness of fit of In (over(f, ̃), over(g, ̃)) 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.

KW - Classification statistics

KW - Discriminant analysis

KW - Normalized power transfer functions

KW - Spectral density

KW - Stable process

UR - http://www.scopus.com/inward/record.url?scp=56949097775&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=56949097775&partnerID=8YFLogxK

U2 - 10.1016/j.stamet.2008.04.003

DO - 10.1016/j.stamet.2008.04.003

M3 - Article

AN - SCOPUS:56949097775

VL - 6

SP - 82

EP - 96

JO - Statistical Methodology

JF - Statistical Methodology

SN - 1572-3127

IS - 1

ER -