Nonlinear Dynamics in Financial Markets: Evidence and Implications
Daily asset returns exhibit two key statistical properties. Returns are not autocorrelated. But the absolute value of returns are strongly autocorrelated. Nonlinear processes can generate this type of behavior, while linear processes cannot. This paper investigates two types of nonlinear processes. Additively nonlinear processes are consistent with the view that expected returns are time varying. While much effort has been applied to modeling expected returns, there has been little evidence to support the view that time varying expected returns can account for the strong nonlinearity in the observed returns data. Multiplicatively nonlinear models are consistent with the view that expected volatilities are time varying. Evidence from price changes as well as options implied volatilities show that volatility is time varying and mean reverting. In fact, multiplicatively nonlinear models have been able to explain a great deal of the nonlinearity in asset returns. Thus, it is possible to forecast future volatility, even though it is difficult to forecast the direction of price changes. This has important implications for short term financial risk management.