Nonlinear Dynamic Structures

The paper develops an approach for analyzing the dynamics of a nonlinear time series that is represented by a nonparametric estimate of its one-step ahead conditional density. The approach entails examination of conditional moment profiles corresponding to certain shocks; a conditional 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 profiles is the nonlinear analog of conventional impulse-response analysis. The approach includes strategies for laying out realistic perturbation experiments in multivariate situations and for undertaking statistical inference using bootstrap methods. It also includes examination of profile bundles for evidence of damping or persistence. The empirical work investigates a bivariate series comprised of daily changes in the Standard and Poor's composite price index and daily NYSE transactions volume from 1928 to 1987. The effort uncovers evidence showing the heavily damped character of the "leverage effect" and the differential response (short-term increase, long-term decline) of trading volume to "common-knowledge" price shocks.