Extreme Event Modelling and Forecasting: Empirical Evidence from Predicting GDP and Unemployment in the USA
Highlights
- The COVID-19 shock in 2020 and the 2008 financial crisis emerged as the most influential extreme events affecting U.S. GDP and unemployment during the period examined.
- Machine-learning and hybrid forecasting approaches, especially Gradient Boosting and ensemble-based models, generally outperformed traditional time-series methods in capturing nonlinear extreme event effects.
- Forecasting models of economic disruption should incorporate crisis-sensitive bottleneck variables such as pandemic-related losses, industrial-sector disruption, DJIA movements, and federal interest-rate changes.
- Combining traditional time-series methods with flexible machine learning models can improve the forecasting of unstable macroeconomic behaviour during rare shocks.
Abstract
1. Introduction
2. The Pertinent Literature
3. Methodology
4. Results and Discussions
5. Conclusions and the Future Directions
Author Contributions
Funding
Data Availability Statement
Conflicts of Interest
References
- Makridakis, S.; Hibon, M. The M3-Competition: Results, conclusions and implications. Int. J. Forecast. 2000, 16, 451–476. [Google Scholar] [CrossRef] [Scilit]
- Assimakopoulos, V.; Nikolopoulos, K. The theta model: A decomposition approach to forecasting. Int. J. Forecast. 2000, 16, 521–530. [Google Scholar] [CrossRef] [Scilit]
- Nikolopoulos, K.; Bougioukos, N.; Giannelos, K.; Assimakopoulos, V. Estimating the impact of shocks with artificial neural networks. In Artificial Neural Networks—ICANN 2007; Lecture Notes in Computer Science; Springer: Berlin/Heidelberg, Germany, 2007; Volume 4669, pp. 476–485. [Google Scholar]
- Taleb, N.N. The Black Swan: The Impact of the Highly Improbable; Random House: New York, NY, USA, 2007. [Google Scholar]
- Armstrong, J.S. Principles of Forecasting: A Handbook for Researchers and Practitioners; Kluwer Academic Publishers: Boston, MA, USA, 2001. [Google Scholar]
- Goodwin, P. Integrating management judgment and statistical methods to improve short-term forecasts. Omega 2002, 30, 127–135. [Google Scholar] [CrossRef] [Scilit]
- Lee, J.K.; Yum, B.J. Judgmental adjustment in time series forecasting using neural networks. Decis. Support Syst. 1998, 22, 135–154. [Google Scholar] [CrossRef] [Scilit]
- Nikolopoulos, K.; Goodwin, P.; Patelis, A.; Assimakopoulos, V. Forecasting with cue information: A comparison of multiple regression with alternative forecasting approaches. Eur. J. Oper. Res. 2007, 180, 354–368. [Google Scholar] [CrossRef] [Scilit]
- Nikolopoulos, K. Forecasting with quantitative methods: The impact of special events in time series. Appl. Econ. 2010, 42, 947–955. [Google Scholar] [CrossRef] [Scilit]
- Romanelli, L.; Figliola, M.A.; Hirsch, F.A. Deterministic chaos and natural phenomena. J. Stat. Phys. 1988, 53, 991–994. [Google Scholar] [CrossRef] [Scilit]
- Golestani, A.; Gras, R. Can we predict the unpredictable? Sci. Rep. 2014, 4, 6834. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Buffa, E.S.; Cosgrove, M.J.; Luce, B.J. An integrated work shift scheduling system. Decis. Sci. 1976, 7, 620–630. [Google Scholar] [CrossRef] [Scilit]
- Horne, J.; Manzenreiter, W. Football Goes East: Business, Culture and the People’s Game in China, Japan and South Korea; Routledge: London, UK, 2004. [Google Scholar]
- Hochreiter, S.; Schmidhuber, J. Long short-term memory. Neural Comput. 1997, 9, 1735–1780. [Google Scholar] [CrossRef] [Scilit]
- Assaad, M.; Boné, R.; Cardot, H. A new boosting algorithm for improved time-series forecasting with recurrent neural networks. Inf. Fusion 2008, 9, 41–55. [Google Scholar] [CrossRef] [Scilit]
- Laptev, N.; Yosinski, J.; Li, L.E.; Smyl, S. Time-series extreme event forecasting at scale. In Proceedings of the International Conference on Machine Learning, Sydney, Australia, 6–11 August 2017; pp. 1–5. [Google Scholar]
- Lin, T.; Horne, B.G.; Tino, P.; Giles, C.L. Learning long-term dependencies in NARX recurrent neural networks. IEEE Trans. Neural Netw. 1996, 7, 1329–1338. [Google Scholar]
- Bengio, Y.; Lamblin, P.; Popovici, D.; Larochelle, H. Greedy layer-wise training of deep networks. In Advances in Neural Information Processing Systems 19; MIT Press: Cambridge, MA, USA, 2006. [Google Scholar]
- Dasgupta, S.; Osogami, T. Nonlinear dynamic Boltzmann machines for time-series prediction. In Proceedings of the Thirty-First AAAI Conference on Artificial Intelligence, San Francisco, CA, USA, 4–9 February 2017; pp. 1833–1839. [Google Scholar]
- Diaconescu, E. The use of NARX neural networks to predict chaotic time series. WSEAS Trans. Comput. Res. 2008, 3, 182–191. [Google Scholar]
- Ding, D.; Zhang, M.; Pan, X.; Yang, M.; He, X. Modeling extreme events in time series prediction. In Proceedings of the 25th ACM SIGKDD International Conference on Knowledge Discovery & Data Mining, Anchorage, AK, USA, 4–8 August 2019; pp. 1114–1122. [Google Scholar]
- Makridakis, S.; Spiliotis, E.; Assimakopoulos, V. Statistical and machine learning forecasting methods: Concerns and ways forward. PLoS ONE 2018, 13, e0194889. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Smyl, S. A hybrid method of exponential smoothing and recurrent neural networks for time series forecasting. Int. J. Forecast. 2020, 36, 75–85. [Google Scholar] [CrossRef] [Scilit]
- Fildes, R.; Makridakis, S. The impact of empirical accuracy studies on time series analysis and forecasting. Int. Stat. Rev. 1995, 63, 289–308. [Google Scholar] [CrossRef] [Scilit]
- Makridakis, S.; Andersen, A.; Carbone, R.; Fildes, R.; Hibon, M.; Lewandowski, R.; Newton, J.; Parzen, E.; Winkler, R. The accuracy of extrapolation/time series methods: Results of a forecasting competition. J. Forecast. 1982, 1, 111–153. [Google Scholar] [CrossRef] [Scilit]
- Makridakis, S.; Chatfield, C.; Hibon, M.; Lawrence, M.; Mills, T.; Ord, K.; Simmons, L.F. The M2-Competition: A re-al-time judgementally based forecasting study. Int. J. Forecast. 1993, 9, 5–22. [Google Scholar] [CrossRef] [Scilit]
- Makridakis, S.; Petropoulos, F.; Spiliotis, E. The M5 competition: Conclusions. Int. J. Forecast. 2022, 38, 1576–1582. [Google Scholar] [CrossRef] [Scilit]
- Makridakis, S.; Spiliotis, E.; Hollyman, R.; Petropoulos, F.; Swanson, N.; Gaba, A. The M6 forecasting competition: Bridging the gap between forecasting and investment decisions. Int. J. Forecast. 2025, 41, 1315–1354. [Google Scholar] [CrossRef] [Scilit]
- Petropoulos, F.; Spiliotis, E. The wisdom of the data: Getting the most out of univariate time series forecasting. Forecasting 2021, 3, 478–497. [Google Scholar] [CrossRef] [Scilit]
- Chapman, J.T.; Desai, A. Macroeconomic predictions using payments data and machine learning. Forecasting 2023, 5, 652–683. [Google Scholar] [CrossRef] [Scilit]
- Le Gal La Salle, J.; David, M.; Lauret, P. A set of new tools to measure the effective value of probabilistic forecasts of continuous variables. Forecasting 2025, 7, 30. [Google Scholar] [CrossRef] [Scilit]
- Assunção, J.B.; Fernandes, P.A. Nowcasting GDP: An application to Portugal. Forecasting 2022, 4, 717–731. [Google Scholar] [CrossRef] [Scilit]
- Tampouris, A.; Dritsaki, C. GDP forecasting with ARIMA, hidden Markov models, and an HMM–LSTM hybrid: Evidence from five economies. Forecasting 2026, 8, 30. [Google Scholar] [CrossRef] [Scilit]
- Aaronson, D.; Brave, S.A.; Butters, R.A.; Fogarty, M.; Sacks, D.W.; Seo, B. Forecasting unemployment insurance claims in realtime with Google Trends. Int. J. Forecast. 2022, 38, 567–581. [Google Scholar] [CrossRef] [Scilit]
- Barbaglia, L.; Frattarolo, L.; Onorante, L.; Pericoli, F.M.; Ratto, M.; Pezzoli, L.T. Testing big data in a big crisis: Nowcasting under COVID-19. Int. J. Forecast. 2023, 39, 1548–1563. [Google Scholar] [CrossRef] [Scilit]
- Hyndman, R.J.; Rostami-Tabar, B. Forecasting interrupted time series. J. Oper. Res. Soc. 2025, 76, 790–803. [Google Scholar] [CrossRef] [Scilit]
- Kynigakis, I.; Panopoulou, E. Modeling the distribution of key economic indicators in a data-rich environment: New empirical evidence. J. Oper. Res. Soc. 2025, 76, 2071–2090. [Google Scholar] [CrossRef] [Scilit]
- Kourentzes, N.; Svetunkov, I. Incorporating risk preferences in forecast selection. J. Oper. Res. Soc. 2026, 1–16. [Google Scholar] [CrossRef] [Scilit]
- Baldwin, R.; di Mauro, B.W. (Eds.) Economics in the Time of COVID-19; Centre for Economic Policy Research: London, UK, 2020. [Google Scholar]
- Brainerd, E.; Siegler, M.V. The Economic Effects of the 1918 Influenza Epidemic; CEPR Discussion Paper No. 3791; Centre for Economic Policy Research: London, UK, 2003. [Google Scholar]
- Barro, R.J.; Ursúa, J.F.; Weng, J. The Coronavirus and the Great Influenza Pandemic: Lessons from the “Spanish Flu” for the Coronavirus’s Potential Effects on Mortality and Economic Activity; NBER Working Paper No. 26866; National Bureau of Economic Research: Cambridge, MA, USA, 2020. [Google Scholar]
- Correia, S.; Luck, S.; Verner, E. Pandemics depress the economy, public health interventions do not: Evidence from the 1918 flu. J. Econ. Hist. 2022, 82, 917–957. [Google Scholar] [CrossRef] [Scilit]
- Jordà, Ò.; Singh, S.R.; Taylor, A.M. Longer-run economic consequences of pandemics. Rev. Econ. Stat. 2022, 104, 166–175. [Google Scholar] [CrossRef] [Scilit]
- Barro, R.J.; Ursúa, J.F. Macroeconomic crises since 1870. Brook. Pap. Econ. Act. 2008, 2008, 255–350. [Google Scholar] [CrossRef] [Scilit]
- Andersen, A.L.; Hansen, E.T.; Johannesen, N.; Sheridan, A. Consumer responses to the COVID-19 crisis: Evidence from bank account transaction data. Scand. J. Econ. 2022, 124, 905–929. [Google Scholar] [CrossRef] [Scilit]
- Lin, Z.; Meissner, C.M. Health vs. Wealth? Public Health Policies and the Economy During COVID-19; NBER Working Paper No. 27099; National Bureau of Economic Research: Cambridge, MA, USA, 2020. [Google Scholar]
- Demirgüç-Kunt, A.; Pedraza, A.; Ruiz-Ortega, C. Banking Sector Performance During the COVID-19 Crisis; World Bank Policy Research Working Paper No. 9363; World Bank: Washington, DC, USA, 2020. [Google Scholar]
- Ivanov, D.; Keskin, B.B. Post-pandemic adaptation and development of supply chain viability theory. Omega 2023, 116, 102806. [Google Scholar] [CrossRef] [Scilit]
- Ivanov, D. Correction to: Viable supply chain model: Integrating agility, resilience and sustainability perspectives—Lessons from and thinking beyond the COVID-19 pandemic. Ann. Oper. Res. 2022, 319, 1411–1431. [Google Scholar] [CrossRef] [Scilit] [PubMed]
- Ivanov, D.; Dolgui, A.; Blackhurst, J.V.; Choi, T.M. Toward supply chain viability theory: From lessons learned through COVID-19 pandemic to viable ecosystems. Int. J. Prod. Res. 2023, 61, 2402–2415. [Google Scholar] [CrossRef] [Scilit]

| Calamity Variable | Role in Model |
|---|---|
| Nominal GDP | Target variable |
| Blizzard damage cost | Not selected |
| Blizzard death toll | Not selected |
| Flood damage cost | Selected predictor |
| Flood death toll | Not selected |
| Hurricane damage cost | Selected predictor |
| Hurricane death toll | Not selected |
| Tornado damage cost | Not selected |
| Tornado death toll | Not selected |
| Wildfire damage cost | Not selected |
| Wildfire death toll | Selected predictor |
| Terrorism damage cost | Not selected |
| Terrorism death toll | Not selected |
| Earthquake damage cost | Not selected |
| Earthquake death toll | Not selected |
| Epidemics/pandemics damage cost | Selected predictor |
| Epidemics/pandemics cases | Not selected |
| Industrial Variable | GDP Model Role | Unemployment-Rate Model Role |
|---|---|---|
| Nominal GDP | Target variable | Not selected |
| Crude oil stock prices | Not selected | Selected predictor |
| AZN stock price | Selected predictor | Not selected |
| Total unemployment rate | Selected predictor | Target variable |
| Auto sales | Not selected | Selected predictor |
| Amazon net income | Not selected | Not selected |
| Number of commercial flights | Selected predictor | Selected predictor |
| Economic Variable | GDP Model Role | Unemployment-Rate Model Role |
|---|---|---|
| Nominal GDP | Target variable | Selected predictor |
| Federal interest rate | Selected predictor | Selected predictor |
| Inflation rate | Selected predictor | Not selected |
| Total unemployment rate | Selected predictor | Target variable |
| DJIA closing value | Selected predictor | Not selected |
| Average Squared Error | ||||||||||
|---|---|---|---|---|---|---|---|---|---|---|
| Model | Dataset | Type of Modelling | ||||||||
| Calamity | Industrial (GDP as Target) | Industrial (Unemployment Rate as Target) | Economic (GDP as Target) | Economic (Unemployment Rate as Target) | Combo Dataset 2 + 3 (GDP as Target) | Combo Dataset 2 + 3 (Unemployment rate as Target) | Predictive | Time Series | Hybrid | |
| MLP | 0.0058 | 0.2922 | 0.2923 | 0.0235 | 0.0448 | 0.0192 | 0.0664 | ✓ | ✕ | ✕ |
| GLM | 0.0060 | 0.2592 | 0.2394 | 0.0367 | 0.5841 | 0.0363 | 0.1243 | ✓ | ✕ | ✕ |
| ORBFEQ | 0.0058 | 0.2656 | 0.2514 | 0.0231 | 0.2879 | 0.0268 | 0.0658 | ✓ | ✕ | ✕ |
| ORBFUN | 0.0059 | 0.2826 | 0.1659 | 0.0271 | 0.0535 | 0.0269 | 0.0511 | ✓ | ✕ | ✕ |
| Decision Tree | 0.0057 | 0.2761 | 0.2394 | 0.0845 | 0.5841 | 0.0401 | 0.1801 | ✓ | ✕ | ✕ |
| Regression | 0.0060 | 0.2592 | 0.2394 | 0.0367 | 0.5841 | 0.0363 | 0.1243 | ✓ | ✕ | ✕ |
| Random Forest | 0.0052 | 0.3038 | 0.2549 | 0.0205 | 0.0828 | 0.0350 | 0.0544 | ✓ | ✕ | ✕ |
| Gradient Boosting | 0.0050 | 0.2869 | 0.2633 | 0.0122 | 0.0413 | 0.0152 | 0.0764 | ✓ | ✕ | ✕ |
| Ensemble | 0.0056 | 0.2389 | 0.1951 | 0.0248 | 0.2015 | 0.0240 | 0.0682 | ✓ | ✕ | ✕ |
| VAR | 0.0078 | 0.2473 | 0.2722 | 0.0074 | 0.7143 | 0.0377 | 0.2629 | ✕ | ✓ | ✕ |
| ES | 0.0047 | 0.0059 | 0.2503 | 0.0059 | 0.2503 | 0.0059 | 0.2603 | ✕ | ✓ | ✕ |
| Best Predictive model | Gradient Boosting | Ensemble | ORBFUN | Gradient Boosting | Gradient Boosting | Gradient Boosting | ORBFUN | |||
| Best Time Series model | ES | ES | ES | ES | ES | ES | ES | |||
| Hybrid Model (Benchmark Predictive Model + Benchmark Time Series Model) | 0.0012 (Gradient Boosting + ES) | 0.0861 (Ensemble + ES) | 0.2129 (ORBFUN + ES) | 0.0229 (Gradient Boosting + ES) | 0.0957 (Gradient Boosting + ES) | 0.0299 (Gradient Boosting + ES) | 0.1662 (ORBFUN + ES) | ✓ | ✓ | ✓ |
| Outlier Table | ||||
|---|---|---|---|---|
| Timeline | Event Description | GDP (% Change) | Unemployment (% Change) | Dataset |
| 11 June | Mississippi River Flood | 0.50% | NA | Calamity (GDP) |
| 17 February | Trump Tax Act + Hurricane Maria, Irma, Harvey | −1% | NA | |
| 19 September | Trade War + Arizona Flood | 1.10% | NA | |
| 8 December | Financial Crisis | NA | 3.80% | Industrial (GDP) |
| 14 September | Quantitative Easing Ends | 4.40% | NA | |
| 20 March | COVID-19 + Financial Crisis | NA | 46.10% | |
| 8 December | Financial Crisis | NA | 277.00% | Industrial (Unemployment rate) |
| 20 March | COVID-19 + Financial Crisis | NA | 319.00% | |
| 8 December | Financial Crisis | NA | 451% | Economy (GDP) |
| 20 March | COVID-19 + Financial Crisis | −39.60% | ||
| 8 December | Financial Crisis | NA | 2% | Economy (Unemployment rate) |
| 14 September | Quantitative Easing Ends | NA | −9.80% | |
| 20 March | COVID-19 + Financial Crisis | −22.40% | NA | |
| 20 March | COVID-19 + Financial Crisis | −43.20% | NA | Combo (GDP) |
| 8 June | Financial Crisis | NA | 149% | Combo (Unemployment) |
| 8 December | Financial Crisis | NA | 368% | |
| 20 March | COVID-19 + Financial Crisis | −22.47% | 143% | |
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Shankar, R.; Alroomi, A.; Bougioukos, V.; Nikolopoulos, K. Extreme Event Modelling and Forecasting: Empirical Evidence from Predicting GDP and Unemployment in the USA. Forecasting 2026, 8, 46. https://doi.org/10.3390/forecast8030046
Shankar R, Alroomi A, Bougioukos V, Nikolopoulos K. Extreme Event Modelling and Forecasting: Empirical Evidence from Predicting GDP and Unemployment in the USA. Forecasting. 2026; 8(3):46. https://doi.org/10.3390/forecast8030046
Chicago/Turabian StyleShankar, R., A. Alroomi, V. Bougioukos, and K. Nikolopoulos. 2026. "Extreme Event Modelling and Forecasting: Empirical Evidence from Predicting GDP and Unemployment in the USA" Forecasting 8, no. 3: 46. https://doi.org/10.3390/forecast8030046
APA StyleShankar, R., Alroomi, A., Bougioukos, V., & Nikolopoulos, K. (2026). Extreme Event Modelling and Forecasting: Empirical Evidence from Predicting GDP and Unemployment in the USA. Forecasting, 8(3), 46. https://doi.org/10.3390/forecast8030046

