A Time Series Analysis of Economical Phenomena in Japan’s Lost Decade (1): Determinacy Property of the Velocity of Money and Equilibrium Solution

The extended velocities of money given by the ratio of NGDP and M<Subscript>2</Subscript>+CD in Japan’s lost decade are analyzed through the non-linear time series analysis based upon the theory of KM<Subscript>2</Subscript>O-Langevin equations. The time series of logarithmic returns of some extended velocities of money are judged to have a determinacy property in a specified time domain whose final time coincides with the time 1999q1 when the Bank of Japan took the zero interest rate policy. This implies that there exists a stochastic process with the time series stated above its realization and it satisfies certain functional relation. This gives a meaning from a viewpoint of time series analysis that the velocity of money can be regarded as an equilibrium solution of the demand and the supply between the goods market and the money market. Copyright Springer Science+Business Media, LLC. 2012