Paper: arXiv 2404.03968

Abstract

The most commonly used form of regularization typically involves defining the penalty function as a L1 or L2 norm. However, numerous alternative approaches remain untested in practical applications. In this study, we apply ten different penalty functions to predict electricity prices and evaluate their performance under two different model structures and in two distinct electricity markets. The study reveals that LQ and elastic net consistently produce more accurate forecasts compared to other regularization types. In particular, they were the only types of penalty functions that consistently produced more accurate forecasts than the most commonly used LASSO. Furthermore, the results suggest that cross-validation outperforms Bayesian information criteria for parameter optimization, and performs as well as models with ex-post parameter selection.

Complexity vs Empirical Score

  • Math Complexity: 3.0/10
  • Empirical Rigor: 8.5/10
  • Quadrant: Street Traders — practical and empirical, lighter on theory

Why this score: The paper applies standard regularization techniques (L1, L2, elastic net, LQ) to an existing forecasting model structure, with relatively simple mathematical exposition, but features extensive empirical rigor using real-world datasets, rolling-window backtests, and detailed statistical performance comparisons.

Research Flowchart

  flowchart TD
  A["Research Goal<br>Test 10 Penalty Functions<br>for Electricity Price Forecasting"] --> B["Methodology<br>Two Markets, Two Model Structures"]
  B --> C{"Cross-Validation Optimization"}
  C --> D["Compute Forecasts<br>LQ & Elastic Net vs. LASSO"]
  D --> E["Key Finding 1<br>LQ & Elastic Net outperform<br>all others & LASSO"]
  C --> F["Alternative Method<br>Bayesian Information Criteria"]
  F --> G["Key Finding 2<br>Cross-Validation superior to<br>BIC & ex-post selection"]
  E --> H["Outcome<br>Standard L1/L2 penalties are suboptimal<br>Specific non-convex penalties improve accuracy"]
  G --> H

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