This paper develops an asymptotic theory for a general class of nonlinear ary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple I(1)...

This paper develops an asymptotic theory for a general class of nonlinear non-stationary regressions, extending earlier work by Phillips and Hansen (1990) on linear cointegrating regressions. The model considered accommodates a linear time trend and stationary regressors, as well as multiple...

While differencing transformations can eliminate nonstationarity, they typically reduce signal strength and correspondingly reduce rates of convergence in unit root autoregressions. The present paper shows that aggregating moment conditions that are formulated in differences provides an orderly...

A number of recently published papers have focused on the problem of testing for a unit root in the case where the driving shocks may be unconditionally heteroskedastic. These papers have, however, assumed that the lag length in the unit root test regression is a deterministic function of the...

Indices of financial returns typically display sample kurtosis that declines towards the Gaussian value 3 as the sampling interval increases. This paper uses stochastic unit root (STUR) and continuous time analysis to explain the phenomenon. Limit theory for the sample kurtosis reveals that...

Two approaches have dominated formulations designed to capture small departures from unit root autoregressions. The first involves deterministic departures that include local-to-unity (LUR) and mildly (or moderately) integrated (MI) specifications where departures shrink to zero as the sample...