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Full Length Research Paper 

A SARIMA Method for Analyzing How 
Agricultural Factors Affect Nigeria's GDP 

Oluremi and Sikiru 

                                    Nnamdi Azikiwe University, Awka Nnewi Agulu, Nigeria 
 

 Accepted 17 January, 2025  

This study uses quarterly data from the first quarter of 2016 to the second quarter of 2022 to assess the impact of 
agricultural factors to Nigeria's overall economic growth and development. The National Bureau of Statistics 
Nigeria provided the information on cattle, forestry, agriculture, and fisheries. The decomposition model (additive 
and multiplication) was fitted using time series analysis and seasonal autoregressive integrated moving average 
(SARIMA). The findings indicated that while the second and third quarters saw higher GDPs than the quarterly 
average, the first and fourth quarters saw lower GDPs from livestock, fisheries, forestry, and crop production (the 
total monetary value of goods produced in years). SARIMA (1,0,1)x(1,0,1)4, SARIMA (2,0,1)x(2,0,1)4, and SARIMA 
(2,0,1)x(2,1,1)4 were all found to be adequate, and any of them may be utilized for additional forecasting. The 
SARIMA model was employed to test for adequacy. Therefore, it is advised that investments in forestry, crop 
production, livestock, and fisheries be made during the second and third quarters of the year in order to reap 
significant benefits. 

Key words: Livestock, Fishery, Forestry, Crop Production, Time Series, SARIMA, Decomposition. 

 
INTRODUCTION 

 

The Agricultural production has long been linked to the production of 

vital food crops, both now and in the past. Forestry, fishing, fruit 

growing, beekeeping, poultry, cattle, and other activities are all 

included in farming. Nowadays, it is accepted that modern agriculture 

includes the processing, marketing, and distribution of crops and 

livestock products, among other things. Therefore, the processing, 

marketing, and distribution of agricultural goods might be considered 

agriculture. It is the foundation of a giving society's economic system 

and is essential to all economies.  

 

Despite the oil boom, Nigeria's economy has grown for decades 

thanks to agriculture, which essentially supplies food, raw materials, 

jobs for a large portion of the population, a source of income for the 

country, a source of livelihood, a significant contribution to 

international trade, marketable surplus, economic development, and a 

source of savings, among other things. In order to attain food 

sufficiency and lower unemployment, the Nigerian government 

continues to rely heavily on agriculture (Anaebonam, 2014).  

 

One globally accepted indicator of economic size and strength is the 

gross domestic product, or GDP (Oyedele, 2017). Nigeria's economy 

can be stimulated by a higher GDP. As a result, it reduced the poverty 

rate among Nigerians by fostering economic growth and job creation. 

During Nigeria's oil boom, the country's agriculture was neglected. In 

actuality, the sector's share of the overall GDP has decreased over time. 

The sector's share of the GDP dropped sharply from 55.8% in 1960–

1970 to 28.4% in 1971–1980. Thankfully, Nigeria's successive 

administrations are starting to prioritize agriculture. Additionally, the 

agricultural sector's share of the GDP increased to 32.3% between 1981 

and 1990, 34.2% between 1991 and 2001, and 40.3% between 2001 and 

2009 (Mohammed, 2012). In 2008, Nigeria's economy was primarily 

driven by agriculture, which accounted for 42.1% of GDP. Industry came 

in second with 22%, followed by wholesale and retail trade with 17.3%, 

services with 16.8%, and building and construction with 1.8%. Over the 

previous 25 years, Nigeria's agricultural sector's contribution of the 

country's GDP has grown by 11.6%, from 30.5% in 1984 to 42.1% in 

2008. At the same time, Nigeria's industry's percentage of the country's 

GDP fell from 42.4% to 22%, a 20.4% drop (Ikoku, 2010).  

 

Through the municipal and state governments, the Nigerian government 

has recently made resources available to assist farmers in obtaining 

fertilizer and other agricultural inputs. The goal of all these initiatives is 

economic diversification. Anono (2012) investigated how the petroleum 

and agricultural sectors contributed to the expansion and advancement of 

the Nigerian economy from 1960 to 2010. They stated that the GDP 

contribution from the agricultural sector was greater than that from the 

petroleum sector. Particularly in the context of developing countries, 

 

 

 

 

African Journal of Agricultural Marketing ISSN: 2375-1061 Vol. 13 (1), pp. 001-006, January, 2025. Available 
online at www.internationalscholarsjournals.org © International Scholars Journals 

Author(s) retain the copyright of this article. 

 
 

http://www.internationalscholarsjournals.org/


2  

growth in the agriculture sector is a predictor of decreasing poverty 

and promoting economic development (Lee, An, & Kim, 2020).  

It is anticipated that rising food costs will have a significant impact on 

the welfare outcomes of various household groups, especially in 

emerging nations, and therefore on their level of poverty and food 

security. By enhancing the overall process of decision-making 

processes, these services also help farmers make better technological 

choices, which in turn leads to a more progressive household for 

these rural farmers as their net revenue increases. Nonetheless, 

numerous studies have demonstrated that farmers with higher levels 

of education are more likely to make more money than those without. 

Because educated farmers have a deeper understanding of a 

particular situation and are equipped with the necessary knowledge 

and awareness, they are able to make decisions that will help them 

earn the money they need to live better. To increase overall "food 

security" and "crop productivity," NGOs and several business sectors, 

particularly in developing nations' agricultural sectors, offer a variety of 

extension services (Sulewski, Wąs, Kobus, Pogodzińska et al., 2020).  

The agricultural sector is essential to the livelihood profile that is 

prevalent in emerging nations, especially in rural areas. The poorest 

people are typically landless and make their living from irregular wage 

labor, which is typically tied to agricultural operations, while the 

majority own or rent a small plot of land that is farmed using traditional 

methods. When rural household farms operate, farming—an 

industry—is created (Ali, 2019).  

 

The high percentage of youth unemployment and the deterioration in 

numerous sectors of the nation, particularly the oil sector, are the 

driving forces behind this study. A country's total progress can be 

accelerated if the government re-strategizes agriculture to increase 

agricultural exports as well as feed the nation. This will result in 

significant financial development and advancement.  

Aim and Objectives 

Estimating the actual contribution of agricultural variables to Nigeria's 

overall economic growth and development is the goal of this study. 

Objectives: 

i. To fit number of Autoregressive 

Integrated Moving Average (ARIMA) 

model to the variable. 

ii. To fit decomposition model. 

To fit Seasonal Autoregressive Integrated Moving Average 
(SARIMA) model on variables. 

 
Literature Review 

Forestry, livestock, fisheries, and crop production are the four main 
subsectors of Nigerian agriculture. Crop production is the largest 
component, accounting for about 87.6% of the sector's total output. 
Fishing, forestry, and cattle follow with 8.1%, 3.2%, and 1.1%, 
respectively. Agriculture remains Nigeria's largest industry, accounting 
for an average of 24% of the nation's GDP over the last seven years 
(2013–2019). Additionally, the industry is the greatest employer in the  
country, employing roughly 36% of the workforce (Oyaniran, 2020).  
Other key economic areas including housing, education, and health 
also received large recurrent sums. Compared to other industries, 
Nigerian public spending on agriculture is rather low; between 2001 

and 2005, less than 2% of all federal spending went into this industry. 
This amount is much less than what is invested in other crucial sectors, 
per a study conducted by the International Food Policy Institute (Aderemi, 
2020).  
 
The 2014 AU Heads of State and Government conference in Equatorial 
Guinea to discuss the Maputo Declaration paved the way for the Malabo 
Declaration. They promised to employ inclusive agricultural growth and 
transformation to cut the continent's poverty in half by 2025, or five years 
from now, and reiterated the 10% public spending target after the Malabo 
meeting. It is anticipated that the agricultural GDP will grow by a 
minimum of 6% every year. They believed that the scheme will give at 
least 30% of young people in agricultural value chains job opportunities 
and empower millions of rural dwellers. Only a small portion of African 
nations have complied with the treaty's terms, though, therefore not much 
has changed thus far (Aderemi, 2020).  
 
Nigeria's first legally required extension policy is now being developed by 
the Federal Department of Agricultural Extension, which was founded in 
2012, with assistance from IFAD21. This new extension policy aims to 
develop the private sector to provide services and the public sector to 
maintain quality control. In order to ensure that extension services are 
driven by demand, consider market demands, and target farmers who 
currently lack access to markets, the focus is on promoting pluralistic 
delivery (Rechard & Olajide, 2020).  
 
Ademola (2019) conducted an experimental evaluation of the impact of 
agricultural funding on the growth of the Nigerian economy. According to 
the study, Nigeria's pace of economic growth is unaffected by the amount 
of credit available to agriculture out of all the credit that the government 
has granted.  
 
Awe (2003) investigated the mobilization of domestic financial resources 
for agricultural productivity in Nigeria using a time series analytic 
technique. The study found that government recurring spending on 
agriculture, bank loans to Nigeria's agricultural sector, and agricultural 
credit programs all positively correlate with agricultural posture. He 
recommended that the government's continuous agricultural spending be 
reassessed increased in order to boost agricultural output.  
 
Ogen (2007) compared the development of Nigeria's agriculture sector to 
that of Brazil's agro-industrial economy between 1960 and 1995. The 
study concluded that Nigeria and other third-world countries need to 
rapidly take advantage of their vast agricultural potential if they are to see 
significant industrial and economic growth.  
 
Olurankinse and Bayo (2012) investigated the impact of non-oil exports 
on Nigeria's economic growth. The findings demonstrated that non-oil 
exports contributed positively to the growth of the Nigerian economy 
during that period, despite its poor performance in terms of output level 
and income generation. They recommended that both the manufacturing 
and agricultural sectors increase production in order to improve product 
availability.  
 
To attain the desired results, a proper system must be maintained. As a 
result, the total output of the rural farmers increases, increasing their 
incomes. The farmers are at the center of any country's agricultural 
system. Numerous countries' governments are also developing a range 
of policies to encourage farmers' contributions to sustainable 
development. In order to boost their net farming income, this incentivizes 
farmers to take greater chances (Ndem & Osondu, 2018).  
 
Bakare (2012) asserts that agriculture is one of Nigeria's main economic 
sectors. The paper states that in order to bring agriculture to a 
sustainable level, Nigerian officials must enact suitable policies.  
Olajide et al. (2012) investigated the relationship between agricultural 
output and Nigeria's GDP. Agriculture and Nigeria's GDP were shown to 



3  

q 

be strongly and favorably correlated by the study.  
 
Akpan (2012) carried out a comparative assessment of the real-world 
impacts of decades of policy practice developed for Nigeria's rural 
communities within the framework of two separate economic eras 
characterized by agricultural output and petroleum oil exploration. The 
results demonstrated the failure of Nigeria's rural development. The 
study concluded that leadership issues, political commitments, and a 
lack of institutional capacity are the main barriers to rural 
development.  
 
Odetola and Etumnu (2013) investigated the role of the agriculture 
sector on Nigeria's economic growth using time series data from 1960 
to 2011 and a growth accounting approach. The analysis confirms the 
agriculture sector's importance in the Nigerian economy by showing 
that it has consistently and favorably increased economic growth.  
Oni (2014) looked into how agriculture helped reduce poverty in 
Nigeria between 1980 and 2011. Oni asserts that agriculture has been 
the primary driver of growth in recent years and has a significant 
potential to reduce poverty in Nigeria. Data from the Augmented 
Dicker Fuller (ADF) unit root test and Error Correction Model (ECM) 
showed that poverty reduction in Nigeria was negatively and 
insignificantly correlated with per capita non-agricultural GDP and 
inflation rate, while it was positively and significantly correlated with 
per capita agriculture GDP, physical infrastructure per capita, and 
social infrastructure per capita. The paper suggests that the 
government should provide Nigerian farmers with the required 
subsidies to enable them to adapt and use modern technologies, 
which will increase productivity and reduce poverty in the nation.  
In order to improve the agricultural system for the country's economic 
growth and sustainable development, many developing countries have 
funded educational and training programs for their rural farmers. The 
goal is to inform them about the current state of affairs and assist 
them in identifying their own values. In these remote areas of rising 
nations, new technologies are also being applied to take the essential 
safeguards before any potentially dangerous event happens (Yu, 
Chen, Niu, Gao et al., 2021).  
 
The results of Olajide, Akinalabi, and Tijani (2012) were at odds with 
those of Lawal (2011). They used an OLS regression model to 
investigate the relationship between Nigeria's GDP and agricultural 
output. They found that Nigeria's GDP is positively and considerably 
impacted by the country's agriculture sector. They also found that 
34.4% of the change in Nigeria's GDP between 1970 and 2010 was 
attributable to the country's agricultural sector.  
Many farmers, especially those in rural parts of the world, are "risk-
averse" because they already have a lot to lose in order to reap the 
expected reward. They do obtain the required output they expected, 
but their risk aversion behavior keeps them from obtaining more. 
According to the "expected utility theory," people who "always prefer 
the expectation E(X) to the random variable X-are characterizable by 
concave utilities" are risk averters (Khaw, Li, & Woodford, 2021).  
Ugwuoke, Ume, and Ihedioha (2018) investigated how interest rate 
deregulation affected agricultural funding in Nigeria between 1970 and 
2014. The study also specifically examined interest rate patterns, loan 
availability to the agricultural sector, and the agricultural sector's GDP 
contribution from 1970 to 2014. The results showed that interest rates 
significantly affect the quantity of credit given to the agricultural sector, 
but they have minimal effect on the industry's GDP contribution. 
Furthermore, it was observed that interest rates varied from 1970 to 
2014, which prompted banks to lend money to the general public while 
also resulting in low agricultural productivity and unemployment. The 
period's rise and downward trends in the agricultural GDP contribution 
can be attributed to the government's disdain when oil was 
discovered.  
 
Materials and Procedures 

The data used in this study was obtained from the first quarter of 2016 to 
the second quarter of 2022 and was provided by the National Bureau of 
Statistics [NBS]. The practice of dissecting time series components to 
evaluate each one's contribution to the time series variable is known as 
time series analysis. The term "decomposition of time series" is 
frequently used to describe this. 
 
Model Details ARIMA Autoregression is incorporated into the moving 
average model. Box and Jenkins (2015) introduced a general model with 
both autoregressive and moving average parameters that specifically 
takes differencing into account in its derivation. Specifically, the model 
contains three types of parameters: the number of differencing runs (d), 
autoregressive parameters (p), and moving average parameters (q). Box 
and Jenkins devised a notation that summarizes models as ARIMA (p, d, 
q). For example, a model with the notation (0, 1, 2) has 0 (zero) 
autoregressive (p) parameters and two moving average (q) parameters 
that were computed for the series after it was differenced once.  
 ARIMA is expressed mathematically as (p, d, q). Φ P (Ls)ϕp (L)zt 
 
SARIMA  
 
Model Seasonal Autoregressive Integrated Moving Averages, or SARIMA 

models. The ARIMA model works well with non-stationary, non-seasonal 

data. Box and Jenkins (1976) have extended this model to account for 

seasonality. Their proposed model is called the Seasonal ARIMA 

(SARIMA) model. This method uses seasonal differencing of the 

appropriate order to remove non-stationarity from the series. The 

difference between an observation and its matching observation from the 

prior year is known as a first order seasonal difference, and it is 

computed as follows:Zt = Yt - Yt-s. For monthly time series 12 = S and for 

quarterly time series 4 = S. This model is generally termed as the 

SARIMA(p,d,q)×(P,D,Q)s model. 

The mathematical formulation of a SARIMA(p,d,q)×(P,D,Q)s model in 

terms of lag polynomials is given below 

Φ P (Ls )ϕp (L)(1− L)d (1− Ls )D yt =ΘQ (Ls )θq (L)εt , 

i.e. Φ P (Ls)ϕp (L)zt =ΘQ (Ls) θ (L)εt. 

 
Results and Discussion 

Multiplicative Model 

Data Gross Domestic Product 

Length 104 

Nmissing 0 

Seasonal Indices 

Period Index 

1 0.88838 

2 1.02261 

3 1.12694 

4 0.96207 

According to the seasonal indices, Q1 GDP was 11.162% below 
the quarterly normal, Q2 GDP was 2.261% higher than the 
quarterly average, Q3 GDP was 12.694% higher than the quarterly 
average, and Q4 GDP was 3.793% lower than the quarterly 
average. 



4  

 
Level of significance: α= 0.05 

Test statistic: Q= n(n+2) ∑𝑘 𝑟2 /(𝑛 − 𝑗)(𝑝 − 𝑣𝑎𝑙𝑢𝑒) 

𝑗=1 𝑗 

Decision rule: Reject Ho if p-value is < α value, otherwise do not 

reject. 

Computation: 

ARIMA Model: Gross Domestic Product Final estimates of 

parameters 

 Type Coef Se Coef T P  Ar 1 0.7910 0.0775 

10.20 0.000 

Sar 4 0.9829 0.0368 26.70 0.000 

Ma 1 -0.2115 0.1164 -1.82 0.072 

Sma 4 0.5311 0.0936 5.67 0.000 

Source: Author’s computation 2024 

Number of observations: 104 

Residuals: SS = 22457028 (backforecasts excluded) MS = 

224570 Df = 100 

Modified Box-Pierce (Ljung-Box) Chi-Square Statistic Lag 12

 24 36 48 

Chi-Square  5.6  7.5 11.5 11.6 

Df 8 20 32 44 

P-Value 0.695 0.995 1.000 1.000 

Source: Author’s computation 2024 

Since p-values are all greater than α value = 0.05, we therefore do 

not reject Ho and conclude that the model is adequate at 5% level of 

significant. 

 

Hypothesis 2 (SARIMA MODEL (2,0,1)4*(2,0,1)) 

HO: The model is adequate. H1: The model is not adequate. Level of 

significance: α= 0.05 

Test statistic: Q = n(n+2) ∑𝑘 𝑟2 /(𝑛 − 𝑗)(𝑝 − 𝑣𝑎𝑙𝑢𝑒) 

𝑗=1 𝑗 

Decision rule: reject Ho if p-value is < α value, otherwise do not reject. 

Computation: 

ARIMA Model: Gross Domestic Product 

Final Estimates of Parameters Type Coef SE Coef T P AR 1 

1.6384 1.4253 1.15 0.253 

AR 2 -0.6748 1.1928 -0.57 0.573 

SAR 4 1.1251 0.2178 5.17 0.000 

SAR 8 -0.1446 0.2064 -0.70 0.485 

MA 1 0.7752 1.4624 0.53 0.597 

SMA 4 0.6340 0.1748 3.63 0.000 

Source: Author’s computation 2024 

Number of Observations: 104 

Residuals: SS = 22902424 (backforecasts excluded) MS = 

233698 DF = 98 

Modified Box-Pierce (Ljung-Box) Chi-Square Statistic Lag 12

 24 36 48 

Chi-Square  7.5  9.9 14.2 14.2 

Df 6 18 30 42 

P-Value 0.280 0.936 0.994 1.000 

Source: Author’s computation 2024 

Since p-values are all greater than the α value =0.05, we therefore, do 

not reject Ho and conclude that the model is adequate and 5% level of 

significant. 

 

Hypothesis 3 (Sarima Model (2,0,1)4*(2,1,1)) Ho: The model is 

adequate. 

H1: The model is not adequate. 

Level of significance: α= 0.05 

Test statistic: Q = n(n+2) ∑𝑘 𝑟2 /(𝑛 − 𝑗)(𝑝 − 𝑣𝑎𝑙𝑢𝑒) 

𝑗=1 𝑗 

Decision rule: reject Ho if p-value is < α value, otherwise do not reject. 

Computation: 

 

Arima Model: Gross Domestic Product 

Final Estimates Of Parameters Type Coef Se Coef T

 P Ar 1 0.3057 0.3613 0.85 0.400 

Ar 2 -0.3062 0.1019 -3.01 0.003 

Sar 4 1.1251 0.1562 7.20 0.000 

Sar 8 -0.1385 0.1482 -0.93 0.352 

Ma 1 0.2556 0.3733 0.68 0.495 

Sma 4 0.7905 0.0962 8.22 0.000 

Source: Author’s computation 2024 

Differencing: 1 regular difference 

Number of observations: original series 104, after differencing 103 

Residuals: SS = 23201644 (back forecasts excluded) 

MS = 239192 DF = 97 

Modified Box-Pierce (Ljung-Box) Chi-Square Statistic Lag 12

 24 36 48 



5  

Chi-Square  7.0  9.2 12.6 12.8 

DF 6 18 30 42 

P-Value 0.317 0.955 0.998 1.000  

Source: Author’s computation 2024 

 
Since p-values are all greater than α value = 0.05, we do not reject Ho 

and conclude that the model is adequate at 5% level of significant. 

 

Measure of Accuracy 

 MULTIPLICATIVE ADDITIVE  

MAPE 802 815  

MAD 1173 1175  

MSD 2335259 2344982  

Source: Author’s computation 2024 

 

The GDP in Q1 was 11.162% below the quarterly average, 2.261% 

above the quarterly average, 12.694% above the quarterly average, 

and 3.793% below the quarterly average in Q2, Q3, and Q4, 

respectively, based on the seasonal indices. All p-values were more 

than the level of significance, suggesting that the model is adequate, 

according to the Ljung-box statistic values for the three tests of data 

adequacy for stationarity time series, SARIMA models. For the 

purposes of this study, SARIMA (1,0,1) ´ (1,0,1)4, SARIMA (2,0,1) ´ 

(2,0,1)4, and SARIMA (2,0,1) ´ (2,1,1) 4 are sufficient. The accuracy 

measure showed that the multiplicative model best fits the data used 

in this study using mean absolute percentage error (MAPE), mean 

absolute deviation (MAD), and mean square deviation (MSD). 

Conclusion 

This study examines the impact of agricultural variables on Nigeria's 

GDP using the SARIMA and decomposition models. The results show 

that the multiplicative model has the lowest value and is the most 

effective. While Q2 and Q3 GDP are often greater than the quarterly 

average and lower in other quarters, the first and fourth quarter GDP 

(gross domestic product, or the total monetary values of items 

generated in a year on livestock, fisheries, forestry, and crop 

production) is lower than the quarterly average. 1,0,1 SARIMA ´ 

(1,0,1)4, 2,0,1 SARIMA ´ (2,0,1)4 Additionally, SARIMA (2,0,1) ´ 

(2,1,1) 4 is determined to be sufficient.This might be applied to 

additional GDP forecasting and prediction. 

 

Recommendations 

 It is recommended that the result be replicated on other 

agricultural data. 

 It is advised that investments be made in livestock, forestry, 
crop production, and fisheries during the second and third 
quarters of the year because the combined monetary values 
of these sectors are higher than the quarterly average. 

 

 It is also recommended that any of the fitted SARIMA models be 

use for forecasting GDP 

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http://www.pwc.com/
http://www.lse.ac.uk/Europeaninstitute/Research/Hellenicobservatory/
https://doi.org/10.1016/j.jclepro.2020.123288

	This study uses quarterly data from the first quarter of 2016 to the second quarter of 2022 to assess the impact of agricultural factors to Nigeria's overall economic growth and development. The National Bureau of Statistics Nigeria provided the infor...
	INTRODUCTION

