Book

About the book

Extreme value theory is the standard framework for extrapolating beyond the observed data. Its classical tools were not built for the high-dimensional, nonstationary, and interconnected systems behind modern risk. This book extends them with Bayesian nonparametrics, information theory, machine learning, and quantum probability, in thirteen chapters and four parts.

Part I covers the generalized extreme value and generalized Pareto distributions with measure-theoretic proofs, and multivariate extremes in high dimensions through angular measures. Part II covers nonparametric tail estimation with boundary bias correction, Bayesian extreme learning with entropy-regularized posteriors, Dirichlet process mixtures for heavy tails, and the Extreme Value Information Criterion for model selection. Part III covers dynamic extreme value models with particle filtering, scoring rules for evaluating and combining forecasts, Pareto-EVaR as a coherent risk measure, and portfolio choice under extremal transfer entropy constraints. Part IV covers causal inference with regularly varying noise, machine learning for extreme quantiles, and quantum density matrices and copulas for systemic risk.

Every theoretical result comes with a complete proof, and every computational method is implemented in R and Python. The applications use stock returns, temperature records, flood data, and cryptocurrency prices. The book is written for researchers, graduate students, and advanced undergraduates in econometrics, finance, environmental science, and risk management.

Contents

Part I. Foundations of Extremes

1. Overview of Extreme Value Theory
2. Multivariate and High-Dimensional Extremes

Part II. Inference Methods

3. Nonparametric and Semiparametric Methods for Extremes
4. Bayesian Inference for Extreme Values
5. Bayesian Nonparametrics for Heavy-Tailed Data
6. Model Selection in Heavy-Tailed Regimes

Part III. Dynamics, Risk, and Forecasting

7. Dynamic Extreme Value Models
8. Evaluation and Combination of Predictive Models
9. Extreme Risk Measures
10. Portfolio Optimization Under Extremes

Part IV. Emerging Frameworks

11. Causal Inference in Tail Regimes
12. Machine Learning for Tail Risk Forecasting
13. Quantum Information Perspectives

Code

Each chapter has R or Python code that reproduces its figures, tables, and case studies.

Related publications

“Capturing information in extreme events”

Economics Letters, 231, 111301 (2023). Chapters 4 and 5.
DOI: 10.1016/j.econlet.2023.111301

“Information content of inflation expectations: A copula-based model”

Studies in Nonlinear Dynamics and Econometrics, 29(1), 71-93 (2024). Chapters 4 and 5.
DOI: 10.1515/snde-2023-0075

“Bayesian extreme value models: Asymptotic behavior, hierarchical convergence, and predictive robustness”

Econometrics and Statistics (2024). Chapters 4 and 5.
DOI: 10.1016/j.ecosta.2024.04.002

“Coherent measure of portfolio risk”

Finance Research Letters, 57, 104222 (2023). Chapter 9.
DOI: 10.1016/j.frl.2023.104222

“Portfolio optimization with transfer entropy constraint”

International Review of Financial Analysis, 96, Part A, 103644 (2024). Chapter 10.
DOI: 10.1016/j.irfa.2024.103644

How to cite

Ardakani, O. M. (2027). Contemporary extreme value methods: Inference, computation, and forecasting. Contributions to Economics. Springer Nature. https://doi.org/10.1007/978-3-032-24915-9

@book{ardakani2027contemporary,
  author    = {Ardakani, Omid M.},
  title     = {Contemporary Extreme Value Methods: Inference, Computation, and Forecasting},
  series    = {Contributions to Economics},
  publisher = {Springer Nature},
  address   = {Cham},
  year      = {2027},
  doi       = {10.1007/978-3-032-24915-9}
}