Some properties of periodically collapsing bubbles

This paper explores some properties of periodically collapsing bubbles, which are a very popular model in the bubbles literature. We first demonstrate that complicated nonlinear bubbles can be represented as a time-varying parameter linear model of order 1. We demonstrate that the bubbles are explosive and nonstationary. We also derive conditions under which the bubbles are strictly stationary. We also demonstrate that the bubbles cannot be weakly stationary by deriving the tail indices of the strictly stationary distribution.