Your use of the JSTOR archive indicates your acceptance of JSTOR's Terms and Conditions of Use, available at

This paper studies the random walk, in a general time series setting that allows for weakly dependent and heterogeneously distributed innovations. It is shown that simple least squares regression consistently estimates a unit root under very general conditions in spite of the presence of autocorrelated errors. The limiting distribution of the standardized estimator and the associated regression t statistic are found using functional central limit theory. New tests of the random walk hypothesis are developed which permit a wide class of dependent and heterogeneous innovation sequences. A new limiting distribution theory is constructed based on the concept of continuous data recording. This theory, together with an asymptotic expansion that is developed in the paper for the unit root case, explain many of the interesting experimental results recently reported in Evans and Savin (1981, 1984).

The paper deals with infinite horizon optimization problems. The existence of optimal solutions is obtained as a consequence of an asymptotic growth condition. We also exhibit finite horizon approximates that yield upper and lower bounds for the optimal values and whose optimal solutions converge to the long-term optimal trajectories.