Testing for stability based on the empirical characteristic funstion with applications to financial data

Abstract

Stable distributions have been widely employed in the last thirty five years to model financial asset returns and other economic variables. However, very few methods have been proposed to test the composite hypothesis of stability and most of these on merely an ad hoc basis. This article presents tests of stability which possess a large-sample level of significance. All tests use the empirical characteristic function. The empirical level and power of the tests are investigated in a series of Monte Carlo experiments which employ models that are popular in the financial literature. The application of the proposed methods to real data leads to reconsideration of prior beliefs regarding the distribution of certain types of financial data.

Keywords:

• Goodness-of-fit test
• simulation
• stable distribution
• stock returns
• symmetric stability