ABSTRACT
In this chapter, we will give a brief history of the Frisch model, and then discuss its theoretical and empirical implications. We will show that the linear deterministic model of business cycles has structural instability. The effect of external noise to a linear oscillator can be studied by the Langevin equation and the Fokker-Planck equation. We may obtain the analytical solution for a harmonic oscillator under Brownian motion. Its exponential decay in amplitude and autocorrelations indicate that white noise is not capable of producing persistent cycles. We can directly estimate the intrinsic frequency and friction coefficient from real US GDP data. We then will discuss the main implications from the Brownian motion of a harmonic oscillator, and basic problems of the linear model of business-cycle theory.
