Common nonlinearities in multiple series of stock market volatility

Decreases in stock market returns often lead to higher increases in volatility than increases in returns of the same magnitude, and it is common to incorporate these socalled leverage effects in GARCH and stochastic volatility models. Recent research has also found it useful to account for leverage in models of realized volatility, as well as in models of the continuous and jump components of realized volatility. This chapter explores the use of smooth transition autoregressive (STAR) models for capturing leverage effects in multiple series of the continuous components of realized volatility. We find that the leverage effect is well captured by a common nonlinear factor driven by returns, even though the persistence in each country?s volatility is country specific. A three-country model that incorporates both country specific persistence and a common leverage effect offers slight forecast improvements for mid-range horizons, relative to other models that do not allow for the common nonlinearity.