Generalized Autoregressive Positive-valued Processes

Bruno Feunou

Journal of Business & Economic Statistics, 2024, vol. 42, issue 2, 786-800

Abstract: 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.

Date: 2024
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DOI: 10.1080/07350015.2023.2239869

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