Several experimental research showed that stock markets display periods of marked turbulence and exhibit extreme values more often than one would expect if the series were normally distributed (fat tail property). In this context, in order to better understand this phenomenon, it was developed, between others, the Markov Switching Model. Nowadays, this kind of models has attached much attention in financial and economic modelling, since, ample empirical evidence has been gathered for both nonlinearity and structural changes in the dynamic properties of many observed time series. We employ a smooth transition autoregressive (STAR) model in order to investigate cyclical behaviour of stock returns in five international stock markets. In the last two decades much attention has been related to modelling the conditional variance. However a point which needs to be stressed it is that an adequate modelling of the nonlinear dependence in the conditional mean is necessary in order to avoid misspecification of the conditional variance model. The results clearly show that the stock markets are characterized by the presence of nonlinear patterns. These findings have important implications for empirical finance, investment decisions, pricing of financial derivatives, portfolio optimization, and cross-market transmission of volatility.

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Nonlinear Time Series, Stock Markets, Volatility.