In his seminal paper, Brooks argues that the relation between return volatility and trading volume can be both linear and nonlinear. Adopting both linear and nonlinear Granger causality tests, he shows that there exists both linear and nonlinear bi-directional causality between trading volumes...

Both stochastic dominance and Omega ratio can be used to examine whether market is efficient, whether there is any arbitrage opportunity in the market, and whether there is any anomaly in the market. In this paper, we first study relationship between stochastic dominance and Omega ratio. We find...