Consider any spectral measure G generated by some stationary stochastic process. We show that there is a deterministic overlapping generations economy whose equilibrium trajectory generates an empirical spectral measure that approximates G. This result shows that linear time series methods cannot observationally differentiate between deterministic and stochastic economies. Our paper relates the above result to recent macroeconomic literature that attempts to model business cycles using low order deterministic "chaotic" difference equations in contrast to the macroeconomic literature that uses low order stable stochastic difference equations. We briefly discuss the problem of observationally distinguishing these two opposing models of the business cycle.