Finite Sample Tests for the Composite Hypothesis of Stable Law

• Activity Number: 144
• Type: Contributed
• Date/Time: Monday, August 4, 2008 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economics Statistics Section
• Author(s): Thomas R. Willemain*+ and Albert S. Paulson and Xin R. Zhong
• Companies: Rensselaer Polytechnic Institute and Rensselaer Polytechnic Institute and
• Keywords: stable law ; finance ; mixture model ; characteristic function

Abstract

Let a random variable be putatively from a stable law. Since sums of stable variates with index alpha are again stable with index alpha, information concerning sums of sample values is captured in powers of the empirical characteristic function (ecf). Scale invariant and nuisance free estimates of alpha are obtained via an application of the Paulson and Delehanty estimation procedure. Excessive differences between the original sample estimate of alpha and the estimates of alpha based on the ecf of sums of values imply rejection of the null hypothesis. We used extensive simulation to produce percentage points of the test for sums of 3 and 10 values and sample sizes 50, 100, 200, 400, 1000. Simulation shows that the test has remarkable power, especially against finite variance alternatives. Financial applications are provided.