Cluster Analysis for Stable Processes

Abstract

It is known that various financial time series, e.g., daily log returns on a share price, foreign exchange rates, excess bond returns, etc., exhibit heavy-tailed behavior. Recently, discriminant analysis has been applied to financial time series, such as, the problem of credit rating for companies. In this article, we investigate the problem of classifying an α-stable linear process into one of two categories with indices α₁ and α₂, respectively. We propose some discriminant criteria. It is shown that our discriminant statistics are consistent. The misclassification probabilities are also evaluated under contiguous hypotheses. Some numerical studies for an (AR(1)) process are given.

Keywords:

• Discriminant analysis
• Functional limit theorem
• Integrated periodogram
• Linear process
• Stable process

Mathematics Subject Classification:

• Primary 62H30
• Secondary 60G52