An asymptotic theory is developed for nonlinear regression with integrated processes. The models allow for nonlinear effects from unit root time series and therefore deal with the case of parametric nonlinear cointegration. The theory covers integrable and asymptotically homogeneous functions. Sufficient conditions for weak consistency are given and a limit distribution theory is provided. The rates of convergence depend on the properties of the nonlinear regression function, and are shown to be as slow as n 1/4 for integrable functions, and to be generally polynomial in n 1/2 for homogeneous functions. For regressions with integrable functions, the limiting distribution theory is mixed normal with mixing variates that depend on the sojourn time of the limiting Brownian motion of the integrated process.

Regulation requiring insiders to publicly disclose their stock trades after the fact complicates the trading decisions of informed, rent-seeking insiders. Given this requirement, we present an insider's equilibrium trading strategy in a multiperiod rational expectations framework. Relative to Kyle (1985), price discovery is accelerated and insider profits are lower. The strategy balances immediate profits from informed trades against the reduction in future profits following trade disclosure and, hence, revelation of some of the insider's information. Our results offer a novel rationale for contrarian trading: dissimulation, a phenomenon distinct from manipulation, may underlie insiders' trading decisions.