Correlation models, such as Constant Conditional Correlation (CCC) GARCH model or Dynamic Conditional Correlation (DCC) GARCH model, play a crucial role in forecasting Value-at-Risk (VaR) or Expected Shortfall (ES). The additional inclusion of constant correlation tests into correlation models has been proven to be helpful in terms of the improvement of the accuracy of VaR or ES forecasts. Galeano & Wied (2017) suggested an algorithms for detecting structural breaks in the correlation matrix whereas Duan & Wied (2018) proposed a residual based testing procedure for constant correlation matrix which allows for time-varying marginal variances. In this chapter, we demonstrate the application of aforementioned correlation testing procedures and compare its performance in backtesting VaR and ES predictions. Portfolios in consideration are constructed from four stock indices DAX30, STOXX50, FTSE100 and S&P.