Generalized Autoregressive Positive-valued Processes

We introduce generalized autoregressive positive-valued (GARP) processes, a class of autoregressive and moving-average processes that extends the class of existing autoregressive positive-valued (ARP) processes in one important dimension: each conditional moment dynamic is driven by a different and identifiable moving average of the variable of interest. The article provides ergodicity conditions for GARP processes and derives closed-form conditional and unconditional moments. The article also presents estimation and inference methods, illustrated by an application to European option pricing where the daily realized variance follows a GARP dynamic. Our results show that using GARP processes reduces pricing errors by substantially more than using ARP processes.