# Limits of Risk Predictability in a Cascading Alternating Renewal Process Model

## TL;DR

This paper introduces the Cascading Alternating Renewal Process (CARP), a model designed to improve risk prediction for interconnected catastrophic events by analyzing prediction accuracy as a function of data size through simulations and real-world data.

## Contribution

The paper presents the CARP model for forecasting interconnected risks and establishes a method to evaluate its prediction precision based on data size, addressing previous limitations.

## Key findings

- Prediction precision improves with more data, following a power law decay.
- CARP accurately recovers parameters in simulated environments.
- Application to real-world data shows potential for global risk prediction.

## Abstract

Most risk analysis models systematically underestimate the probability and impact of catastrophic events (e.g., economic crises, natural disasters, and terrorism) by not taking into account interconnectivity and interdependence of risks. To address this weakness, we propose the Cascading Alternating Renewal Process (CARP) to forecast interconnected global risks. However, assessments of the model's prediction precision are limited by lack of sufficient ground truth data. Here, we establish prediction precision as a function of input data size by using alternative long ground truth data generated by simulations of the CARP model with known parameters. We illustrate the approach on a model of fires in artificial cities assembled from basic city blocks with diverse housing. The results confirm that parameter recovery variance exhibits power law decay as a function of the length of available ground truth data. Using CARP, we also demonstrate estimation using a disparate dataset that also has dependencies: real-world prediction precision for the global risk model based on the World Economic Forum Global Risk Report. We conclude that the CARP model is an efficient method for predicting catastrophic cascading events with potential applications to emerging local and global interconnected risks.