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Title: Unit root and mean reversion in financial time series generated from diffusion models Authors:  Jihyun Kim - Toulouse School of Economics (France) [presenting]
Joon Park - Indiana University (United States)
Abstract: The unit root and mean reversion properties of general diffusion processes and their samples in discrete time are analyzed. In particular, we show that the Dickey-Fuller unit root test has a well-defined limit distribution if, and only if, the underlying diffusion has no mean reversion, while it diverges to minus infinity in probability if, and only if, the underlying diffusion has mean reversion. If applied to the sample from a diffusion model, the test therefore becomes a test for no mean reversion rather than a test for nonstationarity of the underlying diffusion. Diffusion processes are mean-reverting as long as their drift terms play a dominant role, and nonstationary diffusions may well have mean reversion.