# Modelling the Impact of the COVID-19 Pandemic on Some Nigerian Sectorial Stocks: Evidence from GARCH Models with Structural Breaks

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## Abstract

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## 1. Introduction

- i.
- Contribution to the literature of GARCH models with an exogenous variable (in this case, COVID-19).
- ii.
- In-depth study of each sector stock market of Nigeria’s financial market to see how each fared during the COVID-19 pandemic.

## 2. Methodology

#### 2.1. Variants of GARCH Models

#### 2.1.1. The Standard GARCH(p,q) Model

#### 2.1.2. The Asymmetric Power ARCH

#### 2.1.3. GJR-GARCH(p,q) Model

#### 2.1.4. Integrated GARCH(1,1) Model

#### 2.1.5. Threshold GARCH(p,q) Model

#### 2.1.6. Nonlinear GARCH(p,q) Model

#### 2.1.7. EGARCH Model

#### 2.1.8. Absolute Value GARCH Model

#### 2.1.9. Nonlinear Asymmetric GARCH Model

- (i)
- The persistence index of an NAGARCH(1,1) can be seen as $\alpha \left(1+{\delta}^{2}\right)+\beta $ and not simply $\alpha +\beta $ as is common with other GARCH models; and
- (ii)
- The NAGARCH(1,1) model is stationary if $\alpha \left(1+{\delta}^{2}\right)+\beta <1$.

#### 2.2. Persistence and Half-Life Volatility

- (i)
- When $\alpha +{\beta}_{1}<1$, the GARCH model is stationary and has a positive conditional variance.
- (ii)
- When $\alpha +{\beta}_{1}=1$, the model is strictly stationary. In addition, the GARCH model has an exponential decay model which makes the half-life value become infinity.

#### 2.3. Distributions of GARCH Models

## 3. Materials and Methods

## 4. Results

## 5. Discussion

## 6. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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Insurance | Food and Bevarages | Oil and Gas | Banking | Consumer Goods | |
---|---|---|---|---|---|

min: max: median: mean: standard-dev skewness: kurtosis: J-B Test | −0.0826 0.06104 0.00236 0.0015 0.0176 −0.3161 6.135866 Chi-squared: 125.2742 p Value: <2.2 × 10 ^{−16} | −0.0554 0.0565 −0.0002 −0.0003 0.0148 0.0970 7.5910 Chi-squared: 258.2982 p Value: <2.2 × 10 ^{−16} | −0.0587 0.06747 0 0.0002 0.0145 −0.0425 10.27226 Chi-squared: 651.2702 p Value: <2.2 × 10 ^{−16} | −0.1339 0.0769 −0.0003 4.2941e−05 0.0252 −0.8527 7.4399 Chi-squared: 277.7695 p Value: <2.2 × 10 ^{−16} | −0.0908 0.0637 0.0003 0.0003 0.0172 −0.6472 8.0291 Chi-squared: 331.875 p Value: <2.2 × 10 ^{−16} |

Test statistic: | −11.9886 | −11.5032 | −12.0659 | −11.9441 | −11.2705 |

Critical value | −5.08 | −5.08 | −5.08 | −5.08 | −5.08 |

Breakpoint | 261 (20 January 2021) | 60 (26 March 2020) | 142 (27 July 2020) | 50 (23 March 2020) | 57 (23 March 2020) |

Arch Test (lag 15) | ${\chi}^{2}$ = 74.761, df = 15, p-value = 6.253 × 10 ^{−10} | ${\chi}^{2}$ = 36.051, df = 15, p-value = 0.001738 | ${\chi}^{2}$ = 30.743, df = 15, p-value = 0.009507 | ${\chi}^{2}$ = 88.179, df = 15, p-value = 2.166 × 10 ^{−12} | ${\chi}^{2}$ = 85.276, df = 15, p-value = 7.48 × 10 ^{−12} |

Insurance | ||||||
---|---|---|---|---|---|---|

Student t-Distribution | Skewed Student t-Distribution | |||||

Models | AIC | Half-Life | Persistence | AIC | Half-Life | Persistence |

sGARCH(1,1) | −5.430249 | 4.700756 | 0.8629018 | −5.433678 | 4.685996 | 0.8625011 |

gjrGARCH (1,1) | −5.434756 | 3.320903 | 0.8116204 | −5.440714 | 3.933909 | 0.8384519 |

eGARCH (1,1) | −5.435603 | 5.540889 | 0.8824115 | −5.443353 | 6.159152 | 0.8935622 |

apARCH(1,1) | −5.438118 | 3.227181 | 0.8067156 | −5.443518 | 3.653911 | 0.8272072 |

iGARCH(1,1) | −5.423510 | −Inf | 1.0000000 | −5.430062 | −Inf | 1.0000000 |

TGARCH(1,1) | −5.443094 | 3.187461 | 0.8045593 | −5.449578 | 3.700418 | 0.8291817 |

NGARCH(1,1) | −5.415279 | 7.247415 | 0.9087906 | −5.419009 | 10.795367 | 0.9378101 |

NAGARCH (1,1) | −5.434218 | 3.419928 | 0.8165404 | −5.440077 | 4.250878 | 0.8495404 |

AVGARCH(1,1) | −5.436992 | 3.218895 | 0.8062697 | −5.443787 | 3.908028 | 0.8374741 |

Food, Beverages and Tobacco | ||||||
---|---|---|---|---|---|---|

Student t-Distribution | Skewed Student t-Distribution | |||||

AIC | Half-Life | Persistence | AIC | Half-Life | Persistence | |

sGARCH(1,1) | −6.187684 | −1.736062 | 1.4907273 | −6.181459 | −1.711531 | 1.4992826 |

gjrGARCH (1,1) | −6.191418 | −1.719803 | 1.4963648 | −6.184810 | −1.712649 | 1.4988863 |

eGARCH (1,1) | −6.204170 | 11.631495 | 0.9421486 | −6.198026 | 12.052532 | 0.9441120 |

apARCH(1,1) | −6.177988 | NA | NA | −6.179059 | NA | NA |

iGARCH(1,1) | −6.178557 | −Inf | 1.0000000 | −6.172347 | −Inf | 1.0000000 |

TGARCH(1,1) | −6.181729 | 12.360041 | 0.9454638 | −6.175283 | 12.299470 | 0.9452027 |

NGARCH(1,1) | −6.182122 | NA | NA | −6.176249 | NA | NA |

NAGARCH (1,1) | −6.192942 | −2.572041 | 1.3093005 | −6.184288 | −4.106239 | 1.1838874 |

AVGARCH(1,1) | −6.173895 | 13.416227 | 0.9496471 | −6.174778 | 13.949783 | 0.9515255 |

Oil and Gas | ||||||
---|---|---|---|---|---|---|

Student t-Distribution | Skewed Student t-Distribution | |||||

AIC | Half-Life | Persistence | AIC | Half-Life | Persistence | |

sGARCH(1,1) | −6.407924 | 19.71041 | 0.9654446 | −6.402832 | 25.74334 | 0.9734340 |

gjrGARCH (1,1) | −6.414883 | 16.54482 | 0.9589704 | −6.401627 | 28.62948 | 0.9760798 |

eGARCH (1,1) | −6.47725 | 20.33172 | 0.9664827 | −6.495382 | 12.72524 | 0.9469867 |

apARCH(1,1) | −6.395022 | NA | NA | −6.398517 | NA | NA |

iGARCH(1,1) | −6.401054 | −Inf | 1.0000000 | −6.395362 | −Inf | 1.0000000 |

TGARCH(1,1) | −6.400915 | 13.02266 | 0.9481655 | −6.395914 | 12.42958 | 0.9457605 |

NGARCH(1,1) | −6.411548 | NA | NA | −6.401687 | NA | NA |

NAGARCH (1,1) | NA | NA | NA | −6.401862 | 23.18114 | 0.9705413 |

AVGARCH(1,1) | NA | NA | NA | NA | NA | NA |

Banking | ||||||
---|---|---|---|---|---|---|

Student t-Distribution | Skewed Student t-Distribution | |||||

Models | AIC | Half-Life | Persistence | AIC | Half-Life | Persistence |

sGARCH(1,1) | −4.953219 | −8.225464 | 1.0879209 | −4.946755 | −7.966655 | 1.0909033 |

gjrGARCH (1,1) | −4.947277 | −7.488073 | 1.0969864 | −4.940784 | −7.338821 | 1.0990535 |

eGARCH (1,1) | −4.949498 | 11.857763 | 0.9432206 | −4.943097 | 11.894102 | 0.9433890 |

apARCH(1,1) | −4.945765 | NA | NA | −4.939431 | NA | NA |

iGARCH(1,1) | −4.956633 | −Inf | 1.0000000 | −4.950104 | −Inf | 1.0000000 |

TGARCH(1,1) | −4.939225 | 12.750837 | 0.9470902 | −4.932824 | 12.833706 | 0.9474227 |

NGARCH(1,1) | −4.952212 | NA | NA | −4.945352 | NA | NA |

NAGARCH (1,1) | −4.950176 | −7.353524 | 1.0988460 | −4.943644 | −7.378198 | 1.0984997 |

AVGARCH(1,1) | −4.918602 | 22.477988 | 0.9696339 | −4.912585 | 24.508573 | 0.9721144 |

Consumer Goods | ||||||
---|---|---|---|---|---|---|

Student t-Distribution | Student t-Distribution | |||||

Models | AIC | Half-Life | Persistence | AIC | Half-Life | Persistence |

sGARCH(1,1) | −5.764543 | −14.214268 | 1.0499727 | −5.758081 | −14.379034 | 1.0493862 |

gjrGARCH (1,1) | −5.758090 | −14.067359 | 1.0505076 | −5.751610 | −14.259526 | 1.0498102 |

eGARCH (1,1) | −5.774400 | 10.903340 | 0.9384065 | −5.768480 | 11.137049 | 0.9396593 |

apARCH(1,1) | −5.750216 | −1.158048 | 1.8194753 | −5.743754 | −1.114669 | 1.8623544 |

iGARCH(1,1) | −5.769523 | −Inf | 1.0000000 | −5.763061 | −Inf | 1.0000000 |

TGARCH(1,1) | −5.753324 | 14.029914 | 0.9517956 | −5.746889 | 14.202949 | 0.9523687 |

NGARCH(1,1) | −5.756656 | −1.625200 | 1.5318860 | −5.749859 | −1.291511 | 1.7103445 |

NAGARCH (1,1) | −5.759109 | −13.832033 | 1.0513886 | −5.752596 | −13.716094 | 1.0518340 |

AVGARCH(1,1) | −5.746987 | 18.283307 | 0.9627982 | −5.741949 | 12.201455 | 0.9447749 |

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**MDPI and ACS Style**

Adenomon, M.O.; Idowu, R.A.
Modelling the Impact of the COVID-19 Pandemic on Some Nigerian Sectorial Stocks: Evidence from GARCH Models with Structural Breaks. *FinTech* **2023**, *2*, 1-20.
https://doi.org/10.3390/fintech2010001

**AMA Style**

Adenomon MO, Idowu RA.
Modelling the Impact of the COVID-19 Pandemic on Some Nigerian Sectorial Stocks: Evidence from GARCH Models with Structural Breaks. *FinTech*. 2023; 2(1):1-20.
https://doi.org/10.3390/fintech2010001

**Chicago/Turabian Style**

Adenomon, Monday Osagie, and Richard Adekola Idowu.
2023. "Modelling the Impact of the COVID-19 Pandemic on Some Nigerian Sectorial Stocks: Evidence from GARCH Models with Structural Breaks" *FinTech* 2, no. 1: 1-20.
https://doi.org/10.3390/fintech2010001