Price Integration and Adjustment Dynamics Across Global Food Markets: A Multivariate Cointegration Analysis

Buhlebemvelo Dube

doi:10.17306/j.jard.2026.1.00011r1

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Price Integration and Adjustment Dynamics Across Global Food Markets: A Multivariate Cointegration Analysis

Journal of Agribusiness and Rural Development

Volume 79 (2026): Issue 1 (February 2026)

By: Buhlebemvelo Dube

Open Access

|Mar 2026

Figures & Tables

Table 1.

Descriptive statistics of global food price sub-indices (1990–2025)

Variable	Mean	Std. dev.	Minimum	Maximum
Meat	92.71	11.08	74.16	115.78
Dairy	92.38	27.37	51.58	146.28
Cereals	93.70	23.16	64.66	151.33
Oils	97.55	31.52	53.94	183.73
Sugar	88.96	25.14	48.17	144.98

[i] Notes: All indices are expressed on a common FAO reference base. Std. dev. denotes standard deviation.

[ii] Source: author's calculations, 2026.

Table 2.

Correlation matrix of global food price sub-indices (1990–2025)

Variable	Meat	Dairy	Cereals	Oils	Sugar
Meat	1.000
Dairy	0.571^*	1.000
Cereals	0.613^*	0.866^*	1.000
Oils	0.605^*	0.842^*	0.892^*	1.000
Sugar	0.619**	0.547^*	0.674^*	0.637^*	1.000

* denotes statistical significance at the 1% level. Correlation coefficients are based on annual FAO Food Price Index sub-indices.

Source: author's calculations, 2026.

Table 3.

Volatility measures of global food price sub-indices (1990–2025)

Variable	Mean	Std. dev.	Coefficient of variation (CV)	Volatility rank
Oils	97.55	31.52	0.323	1
Dairy	92.38	27.37	0.296	2
Sugar	88.96	25.14	0.283	3
Cereals	93.70	23.16	0.247	4
Meat	92.71	11.08	0.119	5

[i] Notes: The coefficient of variation (CV) is calculated as the ratio of the standard deviation to the mean and provides a scale-independent measure of relative price volatility. Volatility rank is assigned from highest (1) to lowest (5) based on CV values.

[ii] Source: author's calculations, 2026.

Standardised global food price sub-indices (Z-scores)
Source: authors' calculations, 2026.

Levels of FAO Global Food Price sub-indices
Source: author's calculations, 2026.

Table 4.

Augmented Dickey-Fuller unit root test results

Variables	Level		First difference		Order of integration
Variables	T-statistic	5% CV	T-statistic	5% CV	Order of integration
Meat	0.427	−1.950	−4.716	−1.950	I(1)
Dairy	0.619	−1.950	−8.081	−1.950	I(1)
Cereals	−0.180	−1.950	−5.227^*	−1.950	I(1)
Oils	0.027	−1.950	−6.766^*	−1.950	I(1)
Sugar	−0.304	−1.950	−4.871^*	−1.950	I(1)

* denote rejection of the null hypothesis of a unit root at the 10% significance level. All tests are conducted with one lag. Critical values are based on MacKinnon, 1996.

Source: authors' calculations, 2026.

Table 5.

Unit Root Test Results (PP, KPSS)

Variable	PP Statistic (Level)	PP p-value	KPSS Statistic (Level)	Order of integration
Meat	−0.752	0.833	0.630	I(1)
Dairy	−1.642	0.461	0.141	I(1)
Cereals	−2.026	0.275	0.138	I(1)
Oils	−2.214	0.201	0.088	I(1)
Sugar	−2.421	0.136	0.160	I(1)

[i] Notes: The Phillips-Perron (PP) test evaluates the null hypothesis of a unit root, while the KPSS test evaluates the null hypothesis of stationarity. The combined results indicate that all variables are non-stationary in levels. The order of integration is confirmed using ADF tests (reported earlier), where all variables become stationary after first differencing.

[ii] Source: authors' calculations, 2026.

Table 6.

Zivot-Andrews structural break unit root test results

Variable	Test statistic	5% critical value	Break year
Meat	−4.756	−4.800	1998
Dairy	−3.359	−4.800	2015
Cereals	−4.795	−4.800	2007
Oils	−4.419	−4.800	2007
Sugar	−3.999	−4.800	2009

[i] Notes: The Zivot-Andrews test allows for a single endogenous structural break in the intercept. The null hypothesis is the presence of a unit root with a structural break. All test statistics fail to exceed the 5% critical value, indicating that the series remains non-stationary in levels even after accounting for structural breaks.

[ii] Source: authors' calculations, 2026.

Table 7.

Johansen Cointegration Test results

Null hypothesis (r ≤)	Trace statistic	5% critical value
r = 0	83.019	68.520
r = 1	51.019	47.210
r = 2	24.114	29.680
r = 3	9.559	15.410
Null hypothesis	Max-eigen statistic	5% critical value
r = 0 vs r = 1	31.999	33.460
r = 1 vs r = 2	26.905	27.070
r = 2 vs r = 3	14.556	20.970

[i] Source: authors' calculations, 2026.

Table 8.

Vector Error-Correction Model equation diagnostics

Equation	RMSE	R-sq	χ²	P>χ²
D_Meat	5.75054	0.0737	2.148187	0.9512
D_Dairy	17.0363	0.1833	6.061607	0.5326
D_Cereals	12.4852	0.3396	13.88563	0.0533
D_Oils	17.7185	0.5069	27.75723	0.0002
D_Sugar	19.9395	0.0886	2.625833	0.9173

[i] Notes: RMSE denotes root mean squared error. χ² statistics test the joint significance of regressors within each equation.

[ii] Source: authors' calculations, 2026.

Table 9.

VECM Diagnostic Test Results

(a) Serial Correlation: Lagrange Multiplier (LM) Test
Lag Order	Chi-square	Degrees of freedom	p-value	Conclusion
1	36.274	25	0.068	No serial correlation
2	28.953	25	0.266	No serial correlation
(b) Normality of Residuals: Jarque–Bera Test
Equation	Chi-square	p-value
D_Meat	0.961	0.619
D_Dairy	2.831	0.243		Normally distributed
Cereals	0.459	0.795		Normally distributed
D_Oils	2.270	0.321		Normally distributed
D_Sugar	0.290	0.865		Normally distributed
(c) Stability Condition: Eigenvalue Test
Joint Test	6.811	0.743		Residuals jointly normal
Criterion				Result
Maximum modulus of eigenvalues				< 1
Stability condition satisfied				Yes

[i] Notes: The LM test evaluates the null hypothesis of no residual autocorrelation. The Jarque-Bera test assesses normality of residuals at both the equation and system levels. Stability is confirmed when all characteristic roots lie within the unit circle, indicating a dynamically stable VECM.

[ii] Source: authors' calculations, 2026.

Table 10.

Error-correction term estimates (Long-run adjustment speed)

Variable	Coefficient	Std. error	z-statistic	p-value
Meat	1.000	–	–	–
Dairy	2.832	1.108	2.56	0.011
Cereals	1.802	2.064	0.87	0.383
Oils	−5.822	1.124	−5.18	0.000
Sugar	1.672	0.709	2.36	0.018

[i] Source: authors' calculations, 2026.

Impulse Response Functions (IRFs) to a Shock in Vegetable Oil Prices across Global Food Price Sub-Indices
Source: authors' calculations, 2026.

Impulse Response Functions (IRFs) to a Shock in Cereal Prices across Selected Global Food Price Sub-Indices
Source: authors' calculations, 2026.

Table 11.

Forecast Error Variance Decomposition (FEVD) of global food price sub-indices showing relative contributions of own and cross-market shocks

Response variable	Own shock (%)	Oils (%)	Cereals (%)	Dairy (%)	Sugar (%)	Interpretation
Meat	94.2	3.3	1.8	0.1	0.6	Highly isolated
Dairy	74.6	11.8	29.4	–	9.6	Moderately integrated
Cereals	42.8	12.9	–	0.1	10.8	Transmission role
Oils	16.7	–	15.7	0.2	9.7	System driver
Sugar	58.7	30.4	12.6	3.6	–	Partial integration