# Forecasting Facing Economic Shifts, Climate Change and Evolving Pandemics

^{1}

^{2}

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## Abstract

**:**

## 1. What Links Forecasting Economic Shifts, Climate Change and Evolving Pandemics?

## 2. Motivating Examples

## 3. Modeling and Forecasting Linear Stationary Processes

## 4. Failures in Modeling and Forecasting from Shifts of Distributions

## 5. The Optimum: Forecasting Breaks in Advance

- (i)
- the break in question is predictable;
- (ii)
- there is information relevant to that predictability;
- (iii)
- such information is available at the forecast origin;
- (iv)
- there is a forecasting model specification that embodies it;
- (v)
- there is a method for selecting that model from observations;
- (vi)
- the resulting forecasts are usefully accurate.

- (vii)
- the forecasts are acted on in a timely and effective way.

## 6. Some ‘Principles’ for Specifying Forecasting Models

- (I)
- address ‘special features’ like seasonality;
- (II)
- adapt the choice of predictors to the data frequency;
- (III)
- select variables in forecasting models at a loose significance;
- (IV)
- dampen trends and growth rates;
- (V)
- shrink estimates of autoregressive parameters in small samples;
- (VI)
- average across forecasts from ‘non-poisonous’ methods;
- (VII)
- include forecasts from robust devices in that average;
- (VIII)
- update estimates as data arrive, especially after forecast failure;
- (IX)
- do not expect any single method to dominate at all times;
- (X)
- check the implied trend when modeling in differences.

## 7. Forecasting Facing Shifts in Economics

## 8. Forecasting Changes in CO${}_{2}$ Emissions over the Pandemic

## 9. COVID-19 Pandemic Forecasting

## 10. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Notes

1 | Retrospectively, Holliday et al. (2006) showed that the high stress tension in that subduction region was measurable before the earthquake. |

2 | Also see https://voxeu.org/article/predicting-economic-turning-points, (accessed on 4 October 2021). |

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**Figure 1.**(

**a**) Top 1% income shares in the UK since 1918; (

**b**) annual changes in log monthly UK real GDP since 2007; (

**c**) thousand-year changes in atmospheric CO${}_{2}$ in parts per million (ppm) over Ice Ages, and last 250 years; (

**d**) UK daily new confirmed cases of COVID-19 to August 2021.

**Figure 2.**(

**a**) UK annual productivity ${y}_{t}-{l}_{t}$ over 1860-2017; (

**b**) Office of Budget Responsibility (OBR) five-year-ahead forecasts of UK productivity.

**Figure 3.**(

**a**) Actual and fitted values for ${(y-l)}_{t}$ from TIS; (

**b**) scaled residuals; (

**c**) residual density and histogram; (

**d**) trend adjustment of the estimated model given the retained trend indicators.

**Figure 5.**Global daily CO${}_{2}$ emissions 2019–2020 (Mt,

**left**), and percentage change from 52 weeks before (

**right**). Data from carbon monitor.

**Figure 6.**Percentage reduction in daily CO${}_{2}$ emissions from the previous year: aviation (

**left**) and ground transportation (

**right**). Data from carbon monitor.

**Figure 7.**Recursive forecasts of smoothed daily reductions in CO${}_{2}$ during 2020: global emissions (

**left**), international aviation (

**right**). Three forecasting methods: AR(1) (

**first row**); robust AR(1) (

**middle row**); Cardt (

**bottom row**). Data from carbon monitor.

**Figure 8.**(

**a**,

**b**): Cumulative confirmed cases and deaths; (

**c**,

**d**): new cases and deaths with smoothed trends; (

**e**,

**f**): weekly and cumulative vaccinations. Sources: https://coronavirus.data.gov.uk and https://coronavirus.jhu.edu.

**Figure 9.**UK total deaths (left scale; top line) and UK confirmed cases (right scale; middle line), together with real-time average forecasts up to seven days ahead. At the bottom are our full-sample estimates of the R-values, with 95% confidence bands. Period January to August 2021.

**Table 1.**Root mean square error (RMSE; multiplied by 100) and mean absolute percentage error (MAPE) for 1-step ahead forecasts of ${(y-l)}_{t}$ over 2008–2017 and 2010–2017 with recursive estimation.

2008–2017 | 2010–2017 | |||
---|---|---|---|---|

1-Step Forecasts | RMSE | MAPE | RMSE | MAPE |

Without modeling trend breaks (11) | 3.62 | 1.09 | 3.02 | 0.96 |

Robust version of (11) | 1.92 | 0.38 | 0.57 | 0.14 |

With modeling trend breaks (12) | 3.00 | 0.70 | 1.13 | 0.33 |

Robust version of (12) | 2.62 | 0.55 | 0.65 | 0.20 |

Cardt | 1.67 | 0.40 | 0.81 | 0.21 |

**Table 2.**Relative RMSEs and MAPE forecasting the reduction in CO${}_{2}$ emissions 1, 2, 4, and 7 days ahead from 24 January 2020 to 31 December 2020, compared to benchmark AR(1) forecast. <1 indicates smaller RMSE/MAPE than AR(1), with bold denoting smallest out of forecasting models considered.

World Total | Intl. Aviation | EU+ Aviation | US Aviation | World Transport | UK Transport | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

H | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE | RMSE | MAPE |

Robust AR(1) | ||||||||||||

1 | 0.66 | 0.56 | 0.27 | 0.32 | 0.53 | 0.85 | 0.70 | 0.48 | 0.71 | 0.77 | 0.88 | 0.72 |

2 | 0.81 | 0.73 | 0.33 | 0.54 | 0.59 | 0.78 | 0.82 | 0.64 | 0.75 | 0.82 | 0.91 | 0.71 |

4 | 1.03 | 1.14 | 0.44 | 0.48 | 0.63 | 0.83 | 0.83 | 0.89 | 0.78 | 0.92 | 0.91 | 0.91 |

7 | 1.31 | 1.49 | 0.57 | 0.58 | 0.70 | 0.83 | 0.86 | 1.08 | 0.89 | 1.02 | 0.94 | 1.19 |

Cardt | ||||||||||||

1 | 1.29 | 1.48 | 2.75 | 4.20 | 1.50 | 0.95 | 1.19 | 1.78 | 1.17 | 1.07 | 0.99 | 1.18 |

2 | 1.09 | 1.23 | 2.29 | 2.22 | 1.33 | 0.96 | 1.01 | 1.36 | 1.10 | 1.00 | 0.94 | 1.20 |

4 | 0.87 | 0.81 | 1.61 | 2.06 | 1.12 | 0.95 | 0.87 | 0.97 | 0.97 | 0.85 | 0.82 | 1.00 |

7 | 0.63 | 0.61 | 1.08 | 1.36 | 0.80 | 0.96 | 0.64 | 0.76 | 0.69 | 0.71 | 0.60 | 0.77 |

**Table 3.**Coefficients and standard errors (HACSE) from encompassing regressions (13).

World Total | Intl. Aviation | EU+ Aviation | US Aviation | World Transport | UK Transport | |||||||
---|---|---|---|---|---|---|---|---|---|---|---|---|

Coeff | HACSE | Coeff | HACSE | Coeff | HACSE | Coeff | HACSE | Coeff | HACSE | Coeff | HACSE | |

Encompassing model estimates | ||||||||||||

RobAR1 | 0.12 | 0.050 | 0.49 | 0.101 | 0.39 | 0.073 | 0.28 | 0.047 | 0.27 | 0.123 | 0.25 | 0.055 |

Cardt | 0.74 | 0.074 | 0.44 | 0.103 | 0.53 | 0.078 | 0.63 | 0.065 | 0.63 | 0.123 | 0.62 | 0.074 |

World Total | Intl. Aviation | EU+ Aviation | US Aviation | World Transport | UK Transport | |
---|---|---|---|---|---|---|

Averaging Robust AR(1) and Cardt | ||||||

1 | 0.294 | 0.236 | 0.733 | 0.849 | 0.508 | 0.988 |

2 | 0.663 | 0.573 | 1.567 | 1.840 | 0.989 | 1.799 |

4 | 1.413 | 1.552 | 3.117 | 3.310 | 1.889 | 3.261 |

7 | 2.478 | 3.618 | 6.030 | 5.840 | 3.718 | 5.754 |

Dampened Robust AR(1) | ||||||

1 | 0.291 | 0.232 | 0.725 | 0.840 | 0.503 | 0.979 |

2 | 0.655 | 0.566 | 1.541 | 1.814 | 0.971 | 1.778 |

4 | 1.379 | 1.539 | 3.037 | 3.218 | 1.823 | 3.167 |

7 | 2.392 | 3.582 | 5.796 | 5.644 | 3.534 | 5.528 |

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**MDPI and ACS Style**

Castle, J.L.; Doornik, J.A.; Hendry, D.F. Forecasting Facing Economic Shifts, Climate Change and Evolving Pandemics. *Econometrics* **2022**, *10*, 2.
https://doi.org/10.3390/econometrics10010002

**AMA Style**

Castle JL, Doornik JA, Hendry DF. Forecasting Facing Economic Shifts, Climate Change and Evolving Pandemics. *Econometrics*. 2022; 10(1):2.
https://doi.org/10.3390/econometrics10010002

**Chicago/Turabian Style**

Castle, Jennifer L., Jurgen A. Doornik, and David F. Hendry. 2022. "Forecasting Facing Economic Shifts, Climate Change and Evolving Pandemics" *Econometrics* 10, no. 1: 2.
https://doi.org/10.3390/econometrics10010002