TY - JOUR

T1 - Empirical likelihood approach toward discriminant analysis for dynamics of stable processes

AU - Akashi, Fumiya

PY - 2014/7

Y1 - 2014/7

N2 - Discriminant analysis for time series models has been studied by many authors in these few decades, but many of them deal with second order stationary processes. In this paper, we introduce an empirical likelihood statistic based on a Whittle likelihood as a classification statistic, and consider problems of classifying an α-stable linear process into one of two categories described by pivotal quantities θ1 and θ2 of time series models. It is shown that misclassification probabilities by the empirical likelihood criterion converge to 0 asymptotically without assuming that the true model is known. We also evaluate misclassification probabilities when θ2 is contiguous to θ1, and carry out simulation studies to make a comparison between goodness of the empirical likelihood classification statistic and that of an existing method. We observed that the empirical likelihood ratio discriminant statistic performs better than the existing method in some cases even if a family of score functions does not contain the true model. Since the stable processes do not have the finite second moment, this extension is not straightforward, and contains a lot of innovative aspects.

AB - Discriminant analysis for time series models has been studied by many authors in these few decades, but many of them deal with second order stationary processes. In this paper, we introduce an empirical likelihood statistic based on a Whittle likelihood as a classification statistic, and consider problems of classifying an α-stable linear process into one of two categories described by pivotal quantities θ1 and θ2 of time series models. It is shown that misclassification probabilities by the empirical likelihood criterion converge to 0 asymptotically without assuming that the true model is known. We also evaluate misclassification probabilities when θ2 is contiguous to θ1, and carry out simulation studies to make a comparison between goodness of the empirical likelihood classification statistic and that of an existing method. We observed that the empirical likelihood ratio discriminant statistic performs better than the existing method in some cases even if a family of score functions does not contain the true model. Since the stable processes do not have the finite second moment, this extension is not straightforward, and contains a lot of innovative aspects.

KW - Classification statistics

KW - Discriminant analysis

KW - Empirical likelihood ratio

KW - Normalized power transfer functions

KW - Stable process

UR - http://www.scopus.com/inward/record.url?scp=84894453475&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84894453475&partnerID=8YFLogxK

U2 - 10.1016/j.stamet.2014.01.004

DO - 10.1016/j.stamet.2014.01.004

M3 - Article

AN - SCOPUS:84894453475

VL - 19

SP - 25

EP - 43

JO - Statistical Methodology

JF - Statistical Methodology

SN - 1572-3127

IS - 1

ER -