Testing different GARCH models for bull and bear markets

Bull and bear phases were detected for three US stock market indices (S&P 500, Dow Jones Industrial Average, Nasdaq) in the period of 1990/01/01-2020/01/01 and their asymmetric characteristics described and measured. The findings show long steady bull phases interrupted by short and significant bear phasesandwe noted thatthe longest bull phase was followed by the longest bear phase. Acomparison of the ability of symmetric (GARCH) and asymmetric (EGARCH and GJR-GARCH) models to describe the volatility of the detected phases was performed by using the Akaike Information Criterion and the Bayesian Information Criterion. The asymmetric models performed better than the symmetric GARCH model, in particular the EGARCH model was the best model. These results were in line with the findings in the forecast procedure, where the EGARCH model was the best model for the volatility forecast over the entire period whereas the GJR-GARCH model was better for forecasting single phases. In summary, we show evidence of the superiority of asymmetric models when compared to the symmetric GARCH model.