# Climate Risks and Forecasting Stock Market Returns in Advanced Economies over a Century

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## Abstract

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## 1. Introduction

#### 1.1. Climate Change and Finance: Theory and Evidence

#### 1.2. Out-of-Sample Inference Is a Robust Test of Predictability

#### 1.3. Long-Span Data Guard against Sample-Selection Bias

#### 1.4. Many Control Variables and a Machine-Learning Approach

#### 1.5. Summing Up

#### 1.6. Organization of the Study and Its Main Findings

## 2. Data

#### 2.1. Stock Market Data

#### 2.2. Climate Data

#### 2.3. Data on Control Variables

#### 2.4. Sample Period and Summary Statistics

## 3. Methods

#### 3.1. Forecasting Model

#### 3.2. Baseline Estimation Method

#### 3.3. Competing Estimation Methods

#### 3.4. Forecast Evaluation Methods

#### 3.5. Implementation

## 4. Empirical Results

#### 4.1. Full-Sample Results

#### 4.2. Forecasting Results for Stock Market Returns

#### 4.3. Forecasting Results for Stock Market Connectedness

#### 4.4. Lessons from Historical Data

## 5. Concluding Remarks

#### 5.1. Findings and Implications

#### 5.2. Future Research

#### 5.3. Limitations

## Author Contributions

## Funding

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A

Country | Obs | Max | Min | Mean | Median | Std. Dev. |
---|---|---|---|---|---|---|

Canada | 1265 | 20.5891 | −33.4603 | 0.4080 | 0.6870 | 4.5180 |

France | 1265 | 24.2548 | −28.1855 | 0.6252 | 0.6739 | 5.4564 |

Germany | 1265 | 68.8721 | −145.9963 | 0.3085 | 0.4458 | 8.2284 |

Italy | 1265 | 46.8105 | −30.7573 | 0.5354 | 0.1368 | 7.0210 |

Japan | 1265 | 50.8718 | −30.7862 | 0.5303 | 0.5693 | 6.1009 |

Switzerland | 1265 | 28.7773 | −28.2157 | 0.3100 | 0.4851 | 4.3171 |

UK | 1265 | 42.3197 | −30.9241 | 0.3963 | 0.7278 | 4.5539 |

USA | 1265 | 40.7459 | −30.7528 | 0.4710 | 0.9369 | 4.3956 |

Country | Obs | Max | Min | Mean | Median | Std. Dev. |
---|---|---|---|---|---|---|

Canada | 1265 | 147.0692 | 1.4390 | 20.6139 | 15.5299 | 17.4215 |

France | 1265 | 88.9389 | 2.9790 | 29.6710 | 26.5692 | 11.4474 |

Germany | 1265 | 3025.4947 | 19.9740 | 64.9312 | 45.1320 | 121.7298 |

Italy | 1265 | 360.9569 | 6.0676 | 47.8981 | 35.2206 | 43.8551 |

Japan | 1265 | 616.9305 | 7.2515 | 39.0609 | 25.2464 | 51.5448 |

Switzerland | 1265 | 87.4715 | 2.1723 | 19.0636 | 15.5162 | 11.1824 |

UK | 1265 | 385.7659 | 2.0532 | 22.8102 | 16.3587 | 30.0510 |

USA | 1265 | 332.7490 | 4.6791 | 19.3910 | 12.5129 | 24.8187 |

Climate Variable | Obs | Max | Min | Mean | Median | Std. Dev. |
---|---|---|---|---|---|---|

DGT | 1265 | 0.4700 | −0.4800 | 0.0008 | 0.0000 | 0.1216 |

DNHT | 1265 | 0.9600 | −0.8900 | 0.0010 | 0.0000 | 0.2076 |

DGT (GARCH) | 1265 | 0.0488 | 0.0097 | 0.0146 | 0.0132 | 0.0048 |

DNHT (GARCH) | 1265 | 0.4303 | 0.0200 | 0.0456 | 0.0352 | 0.0333 |

Control Variable | Obs | Max | Min | Mean | Median | Std. Dev. |
---|---|---|---|---|---|---|

Oil returns | 1265 | 54.5621 | −56.8125 | 0.2729 | 0.0000 | 6.9743 |

Oil volatility | 1265 | 2992.3046 | 1.0831 | 73.9404 | 25.8844 | 184.8574 |

Gold-to-silver price ratio | 1265 | 114.7485 | 15.1311 | 52.1754 | 47.3461 | 21.3582 |

**Figure A1.**Out-of-sample ${R}^{2}$ statistic for stock market returns (Random Forests). The horizontal axis shows the length of the training window (in percent of the total sample). The vertical axis shows the out-of-sample ${R}^{2}$ statistic. Black line = the rival model includes temperature changes as a potential predictor. Blue line = the rival model includes temperature volatility as a potential predictor. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The parameter h denotes the forecast horizon.

**Figure A2.**Out-of-sample ${R}^{2}$ statistic for stock market returns (absolute forecast errors). The horizontal line shows the length of the training window (in percent of the total sample). The vertical line shows the out-of-sample ${R}^{2}$ statistic (based on absolute forecast errors). Black line = the rival model includes temperature changes as a potential predictor. Blue line = the rival model includes temperature volatility as a potential predictor. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The parameter h denotes the forecast horizon.

**Figure A3.**Out-of-sample $RMSFE$ statistic for stock market returns. RMSFE = root-mean-squared-forecasting error. The horizontal line shows the length of the training window (in percent of the total sample). The vertical line shows the out-of-sample RMSFE statistic (rival vs. benchmark model). Black line = the rival model includes temperature changes as a potential predictor. Blue line = the rival model includes temperature volatility as a potential predictor. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The parameter h denotes the forecast horizon.

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**Figure 2.**Full sample Lasso coefficients. Full sample lasso coefficients as a function of the shrinkage parameter. Black line = coefficient of temperature changes. Blue line = coefficient of temperature volatility. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. Dashed vertical line = shrinkage parameter that minimizes the mean cross-validated error (10-fold cross-validation). The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The parameter h denotes the forecast horizon.

**Figure 3.**Out-of-sample ${R}^{2}$ Statistic for stock market returns. The horizontal axis shows the length of the training window (in percent of the total sample). The vertical axis shows the out-of-sample ${R}^{2}$ statistic. Black line = the rival model includes temperature changes as a potential predictor. Blue line = the rival model includes temperature volatility as a potential predictor. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The parameter h denotes the forecast horizon.

**Figure 4.**Changes in temperature anomalies and volatility. DGT = change in global temperature anomaly. DNHT = change in northern hemisphere temperature anomaly. DGT (GARCH) = volatility of change in the global temperature anomaly. DNHT (GARCH) = volatility of change in the northern hemisphere temperature anomaly.

**Figure 5.**Out-of-sample ${R}^{2}$ statistic for stock market connectedness. The horizontal axis shows the length of the training window (in percent of the total sample). The vertical axis shows the out-of-sample ${R}^{2}$ statistic. Black line = the rival model includes temperature changes as a potential predictor. Blue line = the rival model includes temperature volatility as a potential predictor. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The temperature variables are based on changes in the northern hemisphere temperature anomaly and its volatility. The parameter h denotes the forecast horizon.

Benchmark vs. Rival Model | h = 1 | h = 3 | h = 6 | h = 12 |
---|---|---|---|---|

AR vs. AR plus temperature changes | 0.0237 | 0.0003 | 0.0380 | 0.2465 |

AR vs. AR plus realized volatility | 0.1076 | 0.8562 | 0.0842 | 0.0062 |

AR vs. AR plus temperature changes and realized volatility | 0.0344 | 0.0009 | 0.0011 | 0.0030 |

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## Share and Cite

**MDPI and ACS Style**

Balcilar, M.; Gabauer, D.; Gupta, R.; Pierdzioch, C.
Climate Risks and Forecasting Stock Market Returns in Advanced Economies over a Century. *Mathematics* **2023**, *11*, 2077.
https://doi.org/10.3390/math11092077

**AMA Style**

Balcilar M, Gabauer D, Gupta R, Pierdzioch C.
Climate Risks and Forecasting Stock Market Returns in Advanced Economies over a Century. *Mathematics*. 2023; 11(9):2077.
https://doi.org/10.3390/math11092077

**Chicago/Turabian Style**

Balcilar, Mehmet, David Gabauer, Rangan Gupta, and Christian Pierdzioch.
2023. "Climate Risks and Forecasting Stock Market Returns in Advanced Economies over a Century" *Mathematics* 11, no. 9: 2077.
https://doi.org/10.3390/math11092077