A Test Statistic and Its Application in Modelling Daily Stock Returns

Abstract

In this paper we propose a test statistic to discriminate bctween models with finite variance and models with infinite variance. The test statistic is the ratio of the sample standard deviation and the sample interquartile range. Both asymptotic and finite sample propert,ies of the test statistic are discussed. We show that the test is consistent against infinite-variance distributiorls and has small size distortions. The statistic is applied to compare the competing models for S&P 500 index returns. Our test can not reject most distributions with finite variance for both a pre-crash sample and a post-crash sample, and hence supports the literature. However, for a sample including crash days, our test suggests that the finite-variance distributions must be rejected. The finding is different from what have been discovered in the recent literature.