This paper quantifies tail risks in the outlooks for Canadian inflation and real GDP growth by estimating their conditional distributions at a daily frequency. We show that the tail risk probabilities derived from the conditional distributions accurately reflect realized outcomes during the sample period from 2002 to 2022.
We introduce generalized autoregressive gamma (GARG) processes, a class of autoregressive and moving-average processes in which each conditional moment dynamic is driven by a different and identifiable moving average of the variable of interest. We show that using GARG processes reduces pricing errors by substantially more than using existing autoregressive gamma processes does.