RANDOM-WALKS, BREAKING TREND FUNCTIONS, AND THE CHAOTIC STRUCTURE OF THE VELOCITY OF MONEY

This article examines the times series properties of U.S. velocity series, using Zivot and Andrews's variation of Perron's test. It also tests for deterministic noisy chaos using the Nychka, Ellner, Gallant, and McCaffrey nonparametric test for positivity of the maximum Lyapunov exponent. Comparisons are made among simple-sum and Divisia aggregates using the Thornton and Yue series of Divisia monetary aggregates for an extended sample period (1960:1 to 1992:12). The conclusion is that the unit-root model cannot be rejected even if allowance is made for the possibility of a one-time break in the intercept and the slope of the trend function at an unknown point in time. There is tentative evidence, however, that the Divisia L velocity series is chaotic, implying that (nonlinearity-based) prediction might be possible (at least in the short run and provided that the actual generating mechanism is known exactly).