题目：Testing for Predictability in Continuous Time: A Generalized Likelihood Ratio Approach

主讲人：Wang, Bin, Assistant Professor, Shanghai Jiaotong University

Abstract

This paper develops a test for the presence of predictable components in continuous time models. We allow for nonstationary, as well as stationary, models. The test is based on the generalized likelihood ratio for a very general class of jump di_usion models, and does not require any parametric speci_cations on drift and di_usion functions or jump components. The null hypothesis is formulated as the absence of drift term in a general jump di_usion model. More precisely, our test statistic is de_ned as a normalized version of the generalized likelihood ratio obtained from the approximated Gaussian transition densities under Euler scheme respectively with and without imposing no drift restriction. Our test has standard normal limit distribution under the null hypothesis and has nontrivial powers against properly de_ned local alternatives. Through simulations, we show that our test performs well in _nite samples and, in particular, clearly outperforms the existing tests for martingale di_erences developed in discrete time framework. We also apply our test to thirteen time series including stock price indexes and exchange rates at daily frequency to examine whether or not they have predictable components.