Nonlinear Dynamic Structures
A. Ronald Gallant, Peter E. Rossi, George Tauchen
Econometrica, Vol. 61, No. 4. (Jul., 1993),
pp. 871-907.
Abstract
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.
Keywords: Impulse-response, nonlinear time series,
nonparametric, financial market volatility, trading volume