Co-Movements and Asymmetric Volatility in the Portuguese and U.S. Stock Markets

It has been widely recognised by economists that economic relationships are typically non-linear. This is so that, for example, C. W. J. Granger and T. Teräsvirta [Modelling Nonlinear Economic Relationships, Oxford University Press, New York, 1993], inter alia, have dedicated a whole book to the subject of modelling non-linear economic relationships. Non-linear relationships are present in many aspects of the economic activity, and particularly so in the context of financial markets. Examples of this include the attitude of investors towards the risk and the process of generating financial variables such as stock returns, dividends, interest rates, and so on. On the other hand, the performance of an economy also presents strong signs of a non-linear behaviour: e.g. business cycles, production functions, growth rates, unemployment, etc. Although the shape of non-linearity in these relationships may be rather complex, there are cases where one may admit some sort of linear relationship between the relevant variables within certain regimes. This is the case when one aims to study the co-movements of stock returns volatility and some relevant macroeconomic factors. One obvious question that we may pose in this context is whether the magnitude of positive and negative responses differs for similar positive and negative variations in the predictors, in which case we can say that the underlying variables display asymmetric adjustment. Markets characterised by higher elasticity of supply are likely to show less asymmetry than their counterparts due to increased security of supply. Models of financial markets have incorporated asymmetry using GARCH-type methodologies. An alternative way to deal with these cases is to use threshold autoregressive (TAR) and momentum threshold autoregressive (M-TAR) models to address the problem of multivariate asymmetry. These methodologies are essential when the asymmetric variables are non-stationary (but not only), because of the low power of unit roots and cointegration tests in such cases. In a non-stationary framework, asymmetric cointegration tests were developed by [W. Enders, and P. Siklos, Journal of Business & Economic Statistics19(2), 2001, 166–176] using a modified error correction model derived from the original EG testing procedure. We apply this methodology to the Portuguese and U.S. stock markets using monthly observations from January 1993 to December 2003.