The impact of stationarity assessment on studies of volatility and value-at-risk

Recent research on volatility of asset returns demonstrates that model innovations frequently show unconditional heteroscedasticity. On the other hand, ARMA-GARCH models incorporate the heteroscedasticity only in the conditonal distribution of the innovations, assumng the unconditional distributions to be stationary. Given the observed unconditional heteroscedasticity of the return innovations, there is a need to overcome this shortcoming of existing models. The purpose of this paper is to introduce a test of stationarity of the innovations and show its impact in the analysis of volatility and value at risk. The methodological results are accompanied with examples and simulations.