Testing the climate resilience of sorghum and millet with time series data

Figures & data

Table 1. Descriptive statistics of cereal production

Variable	Millet	Sorghum
Mean	149,898	233,673
Median	154,400	230,000
Min	74,500	106,000
Max	245,550	387,400
S.D	35442.6	81,115
C.V	0.23644	0.347
Skewness	0.152	0.079
Ex. Kurtosis	−0.057	−1.346
No. Data points = 49

Source: Authors’ computation, 2021

Table 2. Preliminary analysis of climate variable

Variable	CO2	Rainfall	Temperature
Mean	0.344	95.546	27.490
Median	0.307	97.410	27.480
Min	0.210	68.863	26.49
Max	0.680	114.090	28.24
S. D	0.114	9.0340	0.422
C.V	0.33022	0.095	0.015
Skewness	1.50	−0.523	−0.486
Kurtosis	1.7153	0.395	−0.085
Number of data points = 49

Source: Author’s Construct, 2021

Table 3. Trend analysis of cereal production

Model	R-Squared	Adj.R^2	AIC	BIC
Millet
Linear	0.331	0.317	1158.935	1152.719
Quadratic	0.335	0.306	1152.296	1156.318
Semi-Log	0.326	0.296	−11.644	−5.968
Sorghum
Linear	0.409	0.397	1224.024	1227.807
Quadratic	0.499	0.478	1217.894	1223.57
Log-linear	0.5	0.47	12.796	18.471

Source: Authors’ Construct, 2021

Figure 1. Trend of millet output from 1970 to 2018.

Figure 2. Trend of sorghum from 1970 to 2018.

The estimated parameters of the best fit trend of the cereals are presented in Table 4.

Table 4. Estimated parameters for the best-fit trend of cereal production

Model	Coefficient	Std. Error	t-ratio	p-value
Millet
Constant	11.616	0.0932	124.700	0.000***
Time	0.013	0.008	1.503	0.1397
Time Squared	6.03247e-05	0.0001	0.3619	0.7191
Sorghum
Constant	11.655	0.119	97.48	0.000***
Time	0.042	0.011	3.817	0.004***
Time-squared	−0.0005	0.0021	−2.326	0.0245**

***, **means significant at 1%, 5% significance level respectively

Source: Authors’ construct, 2021

Table 5. Trend analysis of climate variables

Model	R-Squared	Adj.R2	AIC	BIC
CO2 emission
Linear	0.64	0.632	−121.095	117.311
Quadratic	0.872	0.867	−169.87	164.2
Log-linear	0.872	0.867	−78.495	72.82
Rainfall
Linear	0.01	−0.01	19.601	23.385
Quadratic	0.01	−0.02	358.851	364.526
Log-linear	0.021	−0.022	−84.438	78.762
Temperature
Linear	0.538	0.528	19.601	23.385
Quadratic	0.543	0.523	21.125	26.8
Semi-Log	0.543	0.523	−303.284	−297.608

Source: Authors’ Construct, 2021

Figure 3. Trend of CO₂ emission from 1970 to 2018.

Figure 4. Trend of rainfall from 1970 to 2018.

Figure 5. Trend of temperature from 1970 to 2018.

Table 6. Estimated parameters for the best trend of climate variables

Model	Coefficient	Std. Error	t-ratio	p-value
CO2
Constant	−1.234	0.019	16.94	0.000***
Time	−0.018	0.002	−5.144	0.0002***
Time-squared	0.001	3 × 10^−05	9.146	0.0000***
Rainfall
Constant	4.559	0.044	102.8	0.000***
Time	−0.002	0.004	−0.45	0.65
Time-squared	0.0000005	0.0000007	0.658	0.514
Temperature
Constant	4.559	0.044	102.8	0.000***
Time	−0.001	0.004	−0.456	0.000***
Time Squared	−6.125 × 10°^6	8.50094 × 10^−06	0.658	0.478

***means significant at 1%

Source: Authors’ Construct, 2021

Table 7. KPSS test of the series in levels

	Test with constant		Constant +Trend
Variable	Test-statistic	Critical value	test-statistic	critical value
CO2	1.02	0.471	0.266	0.149
Rainfall	0.136	0.471	0.06	0.149
Temperature	0.941	0.471	0.83	0.149
Millet	0.855	0.471	0.07	0.149
Sorghum	0.79	0.471	0.187	0.149

Source: Authors’ construct, 2021

Table 8. KPSS test of the first difference of the series

	Test with constant		Constant +Trend
Variable	Test-statistic	critical value	Test-statistic	critical value
CO2	0.441	0.471	0.053	0.149
Rainfall	0.038	0.471	0.038	0.149
Temperature	0.086	0.471	0.064	0.149
Millet	0.046	0.471	0.042	0.149
Sorghum	0.106	0.471	0.099	0.149

Source: Authors’ construct, 2021

Table 9. ARDL cointegration test between cereals production and climate variables

	90% level		95% Level		99% level
	I (0)	I (1)	I (0)	I (1)	I (0)	I (1)
Model	2.72	3.77	3.23	4.35	4.29	5.61
	Computed F-Statistics			Decision
Millet and Climate Variables	2.781			No Cointegration
Sorghum and climate variables	0.625			No Cointegration

Source: Authors’ construct, 2021

Table 10. Ljung-box test and ARCH-LM test for models millet and sorghum production and climate variables

	Ljung Box Test		ARCH-LM Test
Model	Test Statistic	P-Value	Test Statistics	P-Value
Millet and Climate Variables	15.572	0.742	19.191	0.509
Sorghum and Climate variables	12.769	0.887	23.784	0.2519

Source: Authors’ Construct, 2021