NONLINEAR DYNAMIC STRUCTURES

The paper develops an approach for analyzing the dynamics of a nonline ar time series that is represented by a nonparametric estimate of its one-step ahead conditional density. The approach entails examination o f conditional moment profiles corresponding to certain shocks; a condi tional moment profile is the conditional expectation evaluated at time t of a time invariant function evaluated at time t + j regarded as a function of j. Comparing the conditional moment profiles to baseline p rofiles is the nonlinear analog of conventional impulse-response analy sis. The approach includes strategies for laying out realistic perturb ation experiments in multivariate situations and for undertaking stati stical inference using bootstrap methods. It also includes examination of profile bundles for evidence of damping or persistence. The empiri cal work investigates a bivariate series comprised of daily changes in the Standard and Poor's composite price index and daily NYSE transact ions volume from 1928 to 1987. The effort uncovers evidence showing th e heavily damped character of the ''leverage effect'' and the differen tial response (short-term increase, long-term decline) of trading volu me to ''common-knowledge'' price shocks.