This study supplies new evidence regarding the predictive power of jumps for conditional market returns and volatilities. We change the constant jump intensity as in the Liu et al. and Du models with time-varying intensity following an autoregressive conditional jump intensity process and a squared Bessel process, and apply calibrated jump premiums to predict excess market returns and volatilities. We show that all calibrated jump premiums have significant predictive power in-sample and out-of-sample. We find that in the US market Liu et al.’s model forecasts excess returns and volatilities better. The autoregressive conditional jump intensity process of jump intensity predicts excess returns better, and the squared bessel process forecasts volatilities better. In the Australian market we find that the model with autoregressive conditional jump intensity process of jump intensity predicts Australian market returns and volatilities better.