Goodness-of-fit tests for continuous-time financial market models

Abstract

This thesis concerns the specification test of diffusion models proposed by A\"{i}t-Sahalia (1996a). A serious doubt on A\"{i}t-Sahalia's test in general and the employment of the kernel method in particular has been cast by Pritsker (1998) by carrying out some simulation studies on A\"{i}t-Sahalia's test. He found that A\"{i}t-Sahalia's test had very poor empirical size relative to nominal size of the test. However, we found that the dramatic size distortion is due to the use of the asymptotic normality of the test statistic. We reformulate the test statistic of A\"{i}t-Sahalia by a version of the empirical likelihood. To speed up the convergence, the bootstrap is employed to find the critical values of the test statistic. The simulation results show that the proposed test has reasonable size and power, which indicate there is nothing wrong with using the kernel method in the test of specification of diffusion models.