Scenario Reduction for Multiple ARMA-Generated Scenarios Using Probability Distance Concepts

In energy system planning and financial risk assessment applications, the Autoregressive Moving Average (ARMA) model is commonly employed to generate numerous scenarios that simulate future uncertainties. However, excessive scenarios can lead to computational burdens, necessitating scenario reduction - the process of selecting the most representative subset from a large generated scenario set while preserving the statistical properties of the original scenario collection.

Probability distance-based scenario reduction methods achieve this by quantifying the "distance" between different scenarios. This distance measurement is not simple geometric distance but rather a metric that reflects the differences between probability distributions of two scenarios. Commonly used probability distances include Kantorovich distance, Wasserstein distance, and other statistical divergence measures.

The implementation approach involves the following computational steps: First, calculate pairwise probability distances between all scenarios to construct a distance matrix using statistical distance functions. Then, employ clustering algorithms (like k-means or hierarchical clustering) or optimization techniques to iteratively merge or remove highly similar scenarios until reaching the predetermined scenario count. During the reduction process, the probability weights of remaining scenarios must be adjusted through weight redistribution algorithms to ensure the reduced scenario set accurately represents the original distribution characteristics.

This methodology not only effectively reduces computational complexity but also preserves key statistical features of the original scenarios, providing a reliable foundation for subsequent decision-making analyses. The implementation typically involves numerical programming with matrix operations for distance calculations and optimization routines for scenario selection.