In this paper, we investigate how Itô's excursion theory can be usefully applied to economic time series data (Itô 2007). We relate excursion theory to geometric and fractional Brownian motion and the Hurst coefficient. We then calculate the Hurst coefficient for all stocks on the DOW 30, S&P...

Purpose – The purpose of this paper is to argue that a stationary-differenced autoregressive (AR) process with lag greater than 1, AR( q 1), has certain properties that are consistent with a fractional Brownian motion (fBm). What the authors are interested in is the investigation of...

Economists who deal with time-series data usually take the unit root test as the ‘prerequisite’ test for a Brownian motion. It is typical for any researchers to apply a battery of well-known unit root tests to their models to confirm stationarity in the model specification. Nonetheless,...