Risk Aggregation Using the Poisson Shot Noise Model: What is the Impact of the Window Size?

• Miguel Angelo Santos Bicudo UFRJ
• Daniel Sadoc Menasché UFRJ

Abstract

The Poisson Shot Noise (PSN) model is a fundamental stochastic process that has been extensively studied for decades. In network communications, for example, understanding the behavior of aggregate flows, which are combinations of multiple constituent flows, is crucial for effective resource provisioning and bandwidth allocation. This work investigates the impact of window size on the inference of PSN parameters. Specifically, we address variance estimation, a key metric in risk aggregation, and assess how varying window sizes influence model accuracy through simulations. Our results suggest that the error in variance estimates follows a square root law, with larger windows reducing the estimation error proportionally to (1/sqrt {w}) . This study provides insights into optimizing window sizes for accurate PSN parameter estimation, which is critical for applications involving non-stationary time series.

Keywords: Poisson Shot Noise, analytical modeling, simulation