Non-linear dependence and conditional heteroscedasticity in stock returns evidence from the norwegian thinly traded equity market

The paper investigates the presence of non-linear dependencies in stock returns for the Norwegian equity market as it is very difficult to interpret the unconditional distribution of stock returns and its economic implications if the i.i.d. assumption is violated. Standard tests of non-linear dependence give strong evidence for the presence of non-linearity in raw returns. Modelling non-linear dependence must distinguish between models that are non-linear in mean and hence depart from the Martingale hypothesis, and models that are non-linear in variance and hence depart from independence but not from the Martingale hypothesis. Therefore, three non-linear models of asset returns are formulated applying ARMA-GARCH specifications for the conditional mean and variance equations. The paper goes on to answer which model has the necessary characteristics that are sufficient to account for most of the non-linear dependence. In the Norwegian equity market most of the non-linear dependence seems to be conditional heteroscedasticity. However, the most thinly traded assets still report significant non-linear dependence for all non-linear specifications. These results imply that the independence hypothesis can be rejected for all assets, portfolios and indices. Moreover, for thinly traded assets the Martingale hypothesis can also be rejected. The economic implications from the unconditional distributions of thinly traded assets are therefore very difficult to interpret and are unfamiliar territory for those who are accustomed to thinking analytically, intuitively and linearly.