Threshold random walks in the US stock market

This paper extends the work in Serletis and Shintani [Serletis A, Shintani M. No evidence of chaos but some evidence of dependence in the US stock market. Chaos, Solitons & Fractals 2003;17:449–54.] and Elder and Serletis [Elder J, Serletis A. On fractional integrating dynamics in the US stock market. Chaos, Solitons & Fractals, forthcoming.] by re-examining the empirical evidence for random walk type behavior in the US stock market. In doing so, it tests the random walk hypothesis by employing unit root tests that are designed to have more statistical power against non-linear alternatives. The non-linear feature of our model is reflected by three regimes, one of which is characterized by a unit root process and the random walk hypothesis while the lower and upper regimes are well captured by a stationary autoregressive process with mean reversion and predictability.