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Bivariate volatility modelling of the impact of crude oil prices on Nigeria exchange rate

International Journal of Statistics and Applied Mathematics · 2026 · Vol. 11(3) · pp. 23–28
Emmanuel Okpanachi✉Haruna Umar Yahaya
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Abstract

This study conducts a bivariate volatility analysis of crude oil prices and Nigeria’s exchange rate using data from 2010 to 2024 (180 observations). It employs descriptive statistics, cross-correlation, Granger causality, Johansen cointegration tests, and both VAR and DBEKK MGARCH frameworks to capture dynamic interactions and volatility persistence. The VAR results show a positive effect of crude oil prices on the exchange rate (0.1574, p = 0.0368) and mean reversion in the exchange rate (−0.158, p = 0.0344), with limited short-run causality at lag 1. DBEKK MGARCH estimates reveal pronounced volatility clustering with asymmetric persistence across series. Crude oil price volatility exhibits strong baseline and ARCH/GARCH dynamics, with A1(1,1) = 0.674 and B1(1,1) = 0.529, while cross-channel instantaneous spillovers are weak (M(1,2) = 0.287, not statistically significant, p = 0.872). The unconditional baseline reflects substantial volatility (M(1,1) = 12.986, p = 0.0216) and a persistent second channel with B1(2,2) = 1.010 and A1(2,2) = 0.286, indicating very strong persistence and long-lasting volatility in that channel. Exchange rate volatility is highly responsive to shocks, with A1(2,2) = 0.286 and B1(2,2) = 1.010, and M(2,2) = -2.474 (p<0.001), suggesting a damping but dominant persistence pattern in the second variance component. The cross-channel influence remains weak under diagonal BEKK, as evidenced by a non-significant M(1,2) and relatively small cross-covariance terms. Overall, a substantial long-run correlation exists between the volatility processes, linking oil-price and currency risks (strong co-movement in volatility). Implications emphasize continuous volatility monitoring and hedging to mitigate persistent risk, and policies to stabilize currency markets and enhance resilience to oil-price shocks through hedging, reserves management, and macroprudential tools.

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Introduction

Crude oil is one of the most valuable and widely traded commodities in the world. It is a complex mixture of hydrocarbons that is refined into various petroleum products, including gasoline, diesel fuel, jet fuel, and lubricants. The first commercial oil well was drilled in 1859 by Edwin Drake in Titusville, Pennsylvania, marking the beginning of the modern oil industry (Yergin, 1991) [42] . Crude oil prices have been a significant factor influencing exchange rates in African countries as the continent is home to several major oil-producing countries, including Nigeria, Angola, and Algeria. A study by Benjamin et al., (2020) [43] using the Johansen cointegration and the vector error correction model to access the dynamic relationship between oil price fluctuations and the real exchange rates in sub-Saharan African countries, demonstrates the significant power of oil prices to predict the movement of real exchange rates in Nigeria, Angola, the republic of Congo, Equatorial Guinea and Gabon. Nigeria as the largest oil producing country in Africa has had its own share of the impact of crude oil prices on its foreign exchange since the discovery of oil in Oloibiri, Nigeria on the 15th January,1956 and its first oil field producing about 5,100 barrels per day (bpd) in 1958. Exchange rate is the price of one currency in terms of another, usually expressed as the number of units one currency can be exchanged for one unit of another currency, according to the international monetary fund (IMF). Fluctuations in global crude oil prices significantly impact Nigeria's economy, including its exchange rates.

Understanding the dynamics between crude oil prices and exchange rates is crucial for policymakers, investors, and stakeholders to make informed decisions.

Materials and Methods

This study adopts a descriptive research design, leveraging a quantitative approach aimed at examining the relationship between crude oil prices and exchange rates in Nigeria. This study will adopt the econometrics models, Vector Autoregressive (VAR) model and Dynamic Baba-Engle-Kraft-Kroner (DBEK) Multivariate Generalized Autoregressive Heteroskedastisity (MGARCH) model to examine this relationship. The VAR model will analyze the dynamic interdependencies over time, while the DBEKK model will examine volatility effects on crude oil prices and exchange rate.

Data collection

This study employs a secondary source of data. The monthly average time series data are collected from the central bank of Nigeria (CBN, www.cbn.gov.ng) spanning from 2010 -2024

Model specification

The VAR introduced by (Christopher sims, 1980) and DBEEK-MGARCH developed by Baba, Engle, Kraft and Kroner in 1990 are adopted in this study. Where: 𝐻 𝑡 is the conditional covariance matrix at time t, 𝛺 𝑡 is a time varying positive definite matrix capturing the baseline variance, 𝐴 𝑖,𝑡 𝑎𝑛𝑑 𝐵 𝑗,𝑡 are time varying matrices representing the dynamic effect associated with past shocks and past covariances, ∈ 𝑡 are the residual errors The VAR model with 179 observations shows the system is stable, with roots around 0.15, indicating shocks decay over time. Crude oil prices have moderate persistence; coefficient ~0.16, p=0.0368, but their lag does not significantly depend on the exchange rate. The exchange rate shows mean reversion; coefficient ~-0.159, p=0.0344, but is unaffected by past oil prices. Residuals are nearly uncorrelated, suggesting minimal contemporaneous shocks. Overall, neither variable significantly influences the other at lag 1, nor the system tends to return to equilibrium over time. Negative and highly significant; in BEKK, a negative M(2,2) can imply a damping or stabilization effect in the second variance component, though interpretation depends on the full matrix structure. Ensure model identification; this term dominates the conditional variance in its path.

The representation of the model specification is as follows

Results and Discussion

Estimation of Volatility Model for Crude oil prices and Exchange rate

From table 5, the diagonal M terms relevant to the baseline variance show a strong positive effect for the first variance component. The cross-term is not supported, and the second diagonal term is strongly negative, suggesting a stabilizing dynamic in the channel within the system.

Conclusion

The results indicate a long-term relationship between the crude oil prices and exchange rates, but short-term causality is limited. Volatility due to shocks persists, highlighting the influence of external factors and policies on their dynamic interaction over time.

Recommendations

Based on the findings, the following recommendations are proposed:

Policy Diversification: Nigeria should diversify its economy to reduce overreliance on oil revenues, which directly influence the exchange rate and economic stability. Promoting sectors like agriculture, manufacturing, and technology can mitigate the adverse effects of oil price volatility.

Acknowledgement

AcknowledgementI acknowledge God Almighty for His help during this research work.

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Market Dynamics and VolatilityMonetary Policy and Economic ImpactFinancial Risk and Volatility ModelingExchange rateCrude oilCointegrationCurrency
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