Citation
Agada, J., Kuhe, D. A., & Anthony, O. N. (2026). An Autoregressive Moving Average Model for Short-Term Prediction of Non-Insulin Dependent Diabetes Among Farmers in Benue State. International Journal of Research, 13(4), 255–278. https://doi.org/10.26643/ijr/edupub/22Style
APA
John Agada1, David Adugh Kuhe 2 and Ojochegbe Noah Anthony 3*
1Department of Mathematics and Computer Science, Rev, Fr. Moses Orshio Adasu University Makurdi, Benue State, Nigeria
2Department of Statistics, Joseph Sarwuan Tarka University, Makurdi, Benue State, Nigeria
3Department of Mathematics and Computer Science, Rev, Fr. Moses Orshio Adasu University Makurdi, Benue State, Nigeria
Corresponding Author: Email: davidkuhe@gmail.com; Tel: 
ABSTRACT
This study employs an Autoregressive Moving Average (ARMA) time series model to forecast the short-term incidence of non-insulin-dependent diabetes mellitus (Type 2 Diabetes) among farmers in Benue State, Nigeria. The data was collected from the Benue State Epidemiological Unit, Makurdi, and covered a 20-year period from January 2005 to June 2025. The study employed descriptive statistics and normality measures, Augmented Dickey-Fuller (ADF) unit root test and ARMA (p,q) model as the principal analytical techniques and procedures used to examine the data. The descriptive statistics indicated moderate variability in diabetes cases over the years, while the Augmented Dickey-Fuller (ADF) test confirmed the stationarity of the series in level. Model choice based on Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC), and Hannan–Quinn Criterion (HQC) identified the ARMA(3,3) model as the best fit for forecasting diabetic cases in the study area. The model’s high coefficient of determination (R² = 0.8905) and statistically significant parameters (p < 0.05) demonstrated its robustness and predictive accuracy. Diagnostic checks using autocorrelation, partial autocorrelation, and the Ljung–Box Q-statistics showed that the residuals behaved like white noise, indicating a well-specified model. Forecast evaluations using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) confirmed that the model accurately good for predicting out-of-sample values. The forecast for July 2025 to June 2027 revealed a potential average of approximately 6,420 diabetes cases per month among farmers, with expected fluctuations over time. The study underscored the growing public health concern of diabetes among the farming population in Benue State and its implications for agricultural productivity and postharvest losses. The study concluded that predictive modeling can serve as a vital tool for health planners to design early intervention strategies, integrate health management with agricultural development, and enhance the overall well-being of rural farmers.
Keywords: Diabetes, ARIMA, Time Series Forecasting, Non-Insulin Dependent Diabetes, Farmers, Benue State, Public Health, Postharvest Losses
1.0 INTRODUCTION
Diabetes mellitus, often simply referred to as diabetes, is a group of metabolic disorders characterized by high blood sugar levels over a prolonged period. The two main types of diabetes are type-1 diabetes, which results from the body’s inability to produce insulin, and Type-2 diabetes develops when the body either becomes resistant to insulin or produces insufficient insulin to control blood sugar levels effectively. Diabetes mellitus is a multifaceted metabolic condition marked by high concentrations of glucose (sugar) in the bloodstream Glucose is a crucial source of energy for cells, and insulin, a hormone produced by the pancreas, plays a central role in regulating its uptake into cells. In diabetes mellitus, this regulation is disrupted, leading to persistent hyperglycemia (high blood sugar) (American Diabetes Association, 2022).
Diabetes mellitus is a significant public health concern worldwide, with its prevalence increasing steadily over the past few decades. According to the International Diabetes Federation (IDF, 2019), an estimated 537 million adults aged 20-79 years were living with diabetes globally in 2021 and this number is projected to rise to 783 million by 2045. The prevalence of diabetes varies by region, with higher rates observed in low- and middle-income countries, particularly in urban areas undergoing rapid socioeconomic development and lifestyle changes. (ADA, 2022).
In Nigeria, the prevalence is estimated at 7% and 11.35% in South-south zone. The Diabetes Association of Nigeria (DAN) reviewed that, mortality rate of diabetes from insufficient management far outweighs that of HIV/AIDs, Malaria and Cancer (Olamoyegun et al., 2024)
Diabetes mellitus is significantly Impacting farmers in Benue State with prevalence rate among yam farming population estimated at 24.9% and mortality rate of 8.61% and as led to reduced labor productivity, economic impact and health complications (Teran, A.D.. 2017)
Diabetes is associated with numerous complications that can affect nearly every organ system in the body. These complications includes Microvascular: Retinopathy (vision loss) neuropathy (nerve damage), nephropathy (kidney damage), and Microvascular: cardiovascular disease (such as heart attack and stroke), others are foot ulcers and amputations. The burden of diabetes-related complications is substantial, leading to increased medical costs, reduced quality of life, and higher risk of premature mortality (ADA, 2022).
Type-2 diabetes, also known as non-insulin dependent diabetes, is a long-term condition that affects how the body processes sugar (glucose), which is an important source of energy. In this condition, the body either becomes resistant to insulin, a hormone that helps move sugar into cells, or doesn’t produce enough insulin to keep blood sugar levels normal (Sun et al., 2021). Unlike type-1 diabetes, where the immune system attacks and destroys insulin-producing cells in the pancreas, type-2 diabetes usually develops slowly over time. While it was once mostly seen in adults, more children and teenagers are now being diagnosed, largely due to increasing obesity and less active lifestyles (Sun et al., 2021).
A major characteristic of type-2 diabetes is insulin resistance, which means the body’s cells don’t respond to insulin as they should. When this happens, the pancreas tries to make more insulin to help move sugar into the cells. However, over time, the pancreas may struggle to keep up with this increased demand. As a result, sugar starts to accumulate in the blood, causing high blood sugar levels (Cloete, 2022).
Several determinants contributes to the risk of developing type-2 diabetes, including obesity, particularly excess fat around the abdomen (central obesity), A sedentary lifestyle, unhealthy eating habits—like eating too many sugary and processed foods—having a family history of diabetes, getting older (especially after 45), and belonging to certain ethnic groups are all factors that can increase the risk of developing diabetes (ADA, 2022).
In Addition to insulin resistance, type-2 diabetes can also involve problems with the pancreas, the organ that makes insulin. Sometimes, the pancreas doesn’t produce enough insulin to keep blood sugar levels in check, making high blood sugar worse (Desai & Deshmukh, 2020).
Symptoms of type-2 diabetes often develop slowly and can include increased thirst, frequent urination, fatigue, blurred vision, slow wound healing, and repeated infections. In the early stages, some people may not notice any symptoms at all, which is why regular screenings are essential (IDF, 2019).
Treatment for type-2 diabetes aims to maintain blood sugar levels within a target range to prevent serious health problems and complications. This typically involves lifestyle modifications such as regular exercise, healthy eating habits (including portion control and selecting nutrient-rich foods), weight management, and monitoring blood sugar levels. (Desai & Deshmukh, 2020).
The management and treatment of type-2 diabetes can impose financial burdens on individuals, families, and healthcare systems. In regions where healthcare costs are primarily borne by the individual or are not adequately covered by insurance, the expenses associated with diabetes care can divert resources away from agricultural investments and productivity-enhancing measures. This can directly impact agricultural communities with reduced investment into agricultural produces, reduced income and crop loss thereby affecting their livelihood (Huang et al., 2016).
Diabetes Mellitus is diagnosed when certain blood sugar levels are met or exceeded. Specifically, a person may be diagnosed if their A1C is 6.5% or higher, which reflects average blood glucose over the past few months. Alternatively, if fasting blood sugar is 126 mg/dL or higher, or if a 2-hour blood sugar reading during an oral glucose tolerance test reaches 200 mg/dL or more, a diagnosis may be made. Additionally, if an individual has a random blood sugar of 200 mg/dL or higher along with symptoms like excessive thirst, frequent urination, or unexplained weight loss, they may also be diagnosed with diabetes (Jaeger et al., 2025).
Agricultural activities, like applying chemical fertilizers and pesticides, can have environmental consequences that can indirectly impact diabetes risk factors. For instance, exposure to chemicals such as glyphosate or organophosphates used in farming has been associated with a higher likelihood of developing metabolic disorders. Additionally, environmental factors such as air pollution and climate change may exacerbate diabetes risk factors and health outcomes, potentially affecting agricultural productivity and crop yields (whiting et al., 2011). Overall, while the direct impact of type-2 diabetes on agricultural productivity and postharvest losses may be limited, the interplay between diabetes, dietary patterns, healthcare access, and environmental factors can have broader implications for agricultural communities and food systems. Addressing the complex relationship between health, agriculture, and the environment requires a holistic approach that considers socioeconomic factors, public health interventions, and sustainable agricultural practices (Whiting et al., 2011).
Overall, while the direct impact of type-2 diabetes on agricultural productivity and postharvest losses may be limited, the interplay between diabetes, dietary patterns, healthcare access, and environmental factors can have broader implications for agricultural communities and food systems. Addressing the complex relationship between health, agriculture, and the environment requires a holistic approach that considers socioeconomic factors, public health interventions, and sustainable agricultural practices (Huang et al., 2016).
This study therefore attempts to extend the existing literature and contribute to the existing body of knowledge by modeling and forecasting non insulin dependent diabetes among farmers in Benue State using autoregressive moving average (ARIMA) time series model with more recent data.
2.0 MATERIALS AND METHODS
2.1 Method of Data Collection
The data utilized in this research work are monthly secondary time series data on morbidity incidence of type-2 diabetes in Benue state for the period of January, 2005 June, 2025 making a total of 234 observations. The data was collected from Benue State Epidemiological unit, Makurdi. The data was transformed to natural logarithms using the following formula:
where 
2.2 Methods of Data Analysis
Find below the statistical tools employed in the analysis of data in this work.
3.2.1 Descriptive statistics and normality measures
The mean of any given set of data can be computed as follows:
The sample standard deviation of any given set of data over a given period of time is computed using the formula:
where 
Jarque-Bera test is a normality test of whether a given sample data have the skewness and kurtosis similar to that of a normal distribution. The test was proposed by Jarque and Bera (1980, 1987) and test the null hypothesis that the series is normally distributed. Given any data set, the test statistic JB is defined as:
where 
and 
whereT is the total number of observations. The JB normality test checks the following pair of hypothesis:
The test rejects the null hypothesis if the p-value of the JB test statistic is less than 
2.2.2 Augmented Dickey-Fuller (ADF) unit root test
The Augmented Dickey-Fuller (ADF) test helps to identify if a time series is stationary or has a unit root, indicating a persistent trend over time (Dickey and Fuller, 1979).
It accounts for higher-order correlations by assuming the series follows an AR(p) process and incorporates lagged differences of the series into the regression to enhance the test’s precision.
.
where 
and evaluated using the conventional 
where 
2.2.3 Portmanteau test
A Portmanteau test also called he Ljung-Box Q-statistic test is used to determine whether there is any remaining serial correlation or autocorrelation in the residuals of a time series. The test checks the following pairs of hypotheses:
where
denotes the autocorrelation estimate of squared standardized residuals at 
2.3 Time Series Models Specification
To specify an ARIMA model which is the model framework use in this study, we first specify autoregressive (AR) model, moving average (MA) model, autoregressive moving average (ARMA) model before specifying autoregressive integrated moving average (ARIMA) model. These models are specified as follows.
2.3.1 The autoregressive (AR) model
A stochastic time series process {
where 
2.3.2 Moving average (MA) model
A time series {
where 
2.3.3 Autoregressive moving average (ARMA) model
A stochastic time series process {
where 
An ARMA (
2.3.4 Autoregressive integrated moving average (ARIMA) model
Autoregressive (AR), Moving Average (MA) or Autoregressive Moving Average (ARMA) model in which differences have been taken are collectively called Autoregressive Integrated Moving Average or ARIMA models. A time series {
Consider then an ARIMA (p, 1, q) process, with 
In terms of the observed series,
2.4 Model Order Selection
We use the following information criteria for model order selection in conjunction with log likelihood function: Akaike information criterion (AIC) due to Akaike (1978), Schwarz information Criterion (SIC) due to (Schwarz, 1978) and Hannan-Quinn information Criterion (HQC) due to (Hannan, 1980). The formula for the information criteria are:
where
Thus given a set of estimated ARMA models for a given set of data, the preferred model is the one with the minimum information criteria and maximum log likelihood.
2.5 Model Forecast Evaluation
We employed Root Mean Square Error (RMSE) and Mean Absolute Error (MAE) accuracy measures to select an optimal model mode that is both parsimonious and accurately forecast the data based on minimum values of the accuracy measures.
2.5.1 Root Mean Square Error (RMSE)
The Root Mean Square Error is a statistical tool for measuring the accuracy of a forecast method. It is computed as:
Where 
2.5.2 Mean Absolute Error (MAE)
The mean absolute error (MAE) is a statistical tool for measuring the average size of the errors in a collection of predictions, without taking their directions into account. It is measured as the average absolute difference between the predicted values and the actual values and is used to assess the effectiveness of a model. It is given as:
where” 
3.0 RESULTS AND DISC0USSION
3.1 Summary Statistics and Normality Measures
This study seeks to provide a short-term prediction of non-insulin-dependent diabetes (Type-2 diabetes mellitus) among farmers in Benue State using the Autoregressive Moving Average (ARMA) time series model. Before model estimation, a preliminary analysis of the dataset was conducted to summarize its key characteristics and assess the normality of the distribution. Table 1 below presents the descriptive statistics and normality test results for the observed monthly diabetes cases.
Table 1: Summary Statistics and Normality Measures
| Variable | Statistic |
| Mean | 5571.321 |
| Maximum | 9661.00 |
| Minimum | 3624.000 |
| Standard Deviation | 1769.088 |
| Skewness | 0.010212 |
| Kurtosis | 1.767498 |
| Jarque-Bera Statistic | 15.57465 |
| p-value | 0.000415 |
| Number of Observations | 246 |
From the result of summary statistics and normality measures reported in Table 1 above, the mean value of approximately 5571 infection cases indicates the average number of recorded non-insulin-dependent diabetes cases among farmers during the study period, while the maximum and minimum values (9661 and 3624, respectively) show the range of variation in the data. The standard deviation (1769) suggests a relatively high level of fluctuation around the mean, implying moderate variability in the monthly incidence of diabetes cases.
The skewness value (0.010212), being close to zero, indicates that the distribution of the series is approximately symmetric. However, the kurtosis value (1.767498) is less than 3, signifying a platykurtic distribution, that is, the data are relatively flatter than a normal distribution with lighter tails.
The Jarque–Bera statistic (15.57465) with an associated p-value of 0.000415 is statistically significant at the 1% level, leading to the rejection of the null hypothesis of normality. This implies that the series does not follow a perfectly normal distribution, which is a common characteristic of real-world time series data.
Overall, the results suggest that while the data are fairly symmetric, they deviate slightly from normality, a factor to be considered when fitting and diagnosing the ARMA model for accurate short-term forecasting.
4.2 Graphical Examination of Diabetes Miletus Series
Examining the morbidity cases of diabetes mellitus is essential for identifying trends and patterns over time, which can provide insights into the progression and fluctuations of the disease within a population. By analyzing these visual representations, healthcare providers and policymakers can better understand peak periods, seasonal variations, and the impact of interventions. This information is crucial for planning targeted healthcare responses, optimizing resource allocation, and developing strategies to reduce disease incidence and manage complications, ultimately improving health outcomes for affected populations. The time plots of the level and log transform series of diabetes mellitus are plotted in Figures 1 and 2 respectively as shown below.
The time plots of the level series and log transformed series reported in Figures 1 and 2 below indicate that both series are covariance or weakly stationary which implies the absence of unit root in the series in level. This is indicated by the smooth trend of both series.
Figure 1: Time Series Plot of Diabetes Miletus in Benue State from 2005 to 2025
Figure 2: Time Series Plot of Natural Log of Diabetes Miletus in Benue State from 2005
to 2025
4.3 Augmented Dickey-Fuller (ADF) Unit Root Test Result
To ensure the appropriateness of applying an Autoregressive Moving Average (ARMA) model for short-term prediction of non–insulin-dependent diabetes cases among farmers in Benue State, it is necessary to examine the time series properties of the data. A key requirement for ARMA modeling is that the underlying series must be stationary. Therefore, the Augmented Dickey–Fuller (ADF) unit root test was conducted to determine whether the series 
The ADF statistics reported in Table 2 below for both model specifications (intercept only and intercept with trend) are -15.3344 and -15.4304, respectively. These values are far more negative than their corresponding 5% critical values (-2.8731 and -3.4283). In addition, the associated p-values are 0.0000, indicating strong statistical significance. Because the ADF test statistics are well below the critical values and the p-values are less than 0.05, the null hypothesis of a unit root is rejected under both model specifications. This confirms that the series 
Table 2: Augmented Dickey-Fuller (ADF) Unit Root Test Result
| Variable | Option | ADF Test Statistic | p-value | 5% Critical Value |
 | Intercept only | -15.3344 | 0.0000 | -2.8731 |
| Intercept & Trend | -15.4304 | 0.0000 | -3.4283 |
4.4 Autocorrelations and Partial Autocorrelations Functions of the Series
After confirming that the series of non–insulin-dependent diabetes cases among farmers in Benue State is stationary, the next step in the ARMA modeling process involves examining the autocorrelation structure of the series. The Autocorrelation Function (ACF) and Partial Autocorrelation Function (PACF) are used to identify the dependence pattern between current and past observations, which guides the selection of appropriate autoregressive (AR) and moving-average (MA) orders.
Furthermore, the Ljung-Box Q-statistics were computed to test for the joint significance of autocorrelations up to various lags. This test determines whether the residuals are independently distributed — a key requirement for model adequacy. Table 3 below presents the ACF, PACF, and Ljung-Box Q-statistics results for the series while Figure 3 belowpresented the ACF and PACF plots of the series.
The results of ACF and PACF reported in Table 3 below and Figure 3 show that the autocorrelation (ACF) and partial autocorrelation (PACF) coefficients for all lags are small in magnitude, fluctuating around zero. This indicates the absence of significant serial correlation in the data. None of the autocorrelations exceed the approximate 95% confidence bounds (±0.1 for a large sample size of 246), suggesting that the time series behaves like a white-noise process.
The Ljung-Box Q-statistics and their corresponding p-values across all lags (p > 0.05) further confirm that there is no significant autocorrelation remaining in the residuals. This means that the null hypothesis of no autocorrelation cannot be rejected at any lag, implying that the series is adequately described by a stationary stochastic process (Ljung & Box, 1979).
Table 3: Autocorrelations and Ljung-Box Q-Statistics Test Results
| Lag | ACF | PACF | Q-Statistics | p-value |
| 1 | 0.014 | 0.014 | 0.0458 | 0.831 |
| 2 | -0.019 | -0.019 | 0.1338 | 0.935 |
| 3 | 0.004 | 0.005 | 0.1380 | 0.987 |
| 4 | -0.049 | -0.050 | 0.7497 | 0.945 |
| 5 | 0.022 | 0.024 | 0.8747 | 0.972 |
| 6 | 0.037 | 0.034 | 1.2165 | 0.976 |
| 7 | 0.022 | 0.023 | 1.3420 | 0.987 |
| 8 | 0.017 | 0.015 | 1.4126 | 0.994 |
| 9 | -0.007 | -0.005 | 1.4260 | 0.998 |
| 10 | -0.110 | -0.107 | 4.5659 | 0.918 |
| 11 | -0.025 | -0.022 | 4.7227 | 0.944 |
| 12 | 0.078 | 0.075 | 6.2944 | 0.901 |
| 13 | -0.008 | -0.012 | 6.3115 | 0.934 |
| 14 | -0.017 | -0.027 | 6.3907 | 0.956 |
| 15 | 0.052 | 0.055 | 7.0970 | 0.955 |
| 16 | -0.035 | -0.022 | 7.4226 | 0.964 |
| 17 | -0.012 | -0.008 | 7.4599 | 0.977 |
| 18 | -0.088 | -0.093 | 9.5213 | 0.946 |
| 19 | -0.054 | -0.050 | 10.302 | 0.945 |
| 20 | -0.092 | -0.114 | 12.567 | 0.895 |
| 21 | -0.026 | -0.032 | 12.750 | 0.917 |
| 22 | -0.115 | -0.115 | 16.369 | 0.797 |
| 23 | 0.007 | 0.008 | 16.381 | 0.838 |
| 24 | -0.053 | -0.074 | 17.165 | 0.842 |
| 25 | -0.056 | -0.036 | 18.032 | 0.841 |
| 26 | -0.047 | -0.056 | 18.643 | 0.851 |
| 27 | 0.055 | 0.057 | 19.482 | 0.852 |
| 28 | -0.011 | -0.032 | 19.514 | 0.882 |
| 29 | 0.060 | 0.057 | 20.511 | 0.876 |
| 30 | 0.056 | 0.042 | 21.381 | 0.876 |
| 31 | 0.040 | 0.061 | 21.828 | 0.888 |
| 32 | -0.001 | -0.015 | 21.828 | 0.912 |
| 33 | -0.027 | -0.007 | 22.036 | 0.927 |
| 34 | -0.109 | -0.121 | 25.432 | 0.855 |
| 35 | -0.056 | -0.074 | 26.342 | 0.854 |
| 36 | 0.066 | 0.025 | 27.604 | 0.841 |
Figure 3: Plots of ACF and PACF of Log Transformed Series
Collectively, these findings suggest that the series is not driven by persistent temporal dependence, and any ARMA model fitted to the data should yield uncorrelated and well-behaved residuals. Therefore, the dataset is suitable for ARMA model identification and estimation, and the absence of significant autocorrelation validates the appropriateness of proceeding with short-term forecasting using the ARMA framework.
4.5 Model Order Selection
Following the establishment of stationarity and the absence of significant autocorrelation in the diabetes time series, various ARMA model orders were estimated to determine the most parsimonious and best-fitting specification for short-term prediction. Model selection was based on several statistical criteria, including the Log Likelihood (LogL), Akaike Information Criterion (AIC), Schwarz Information Criterion (SIC), and Hannan–Quinn Criterion (HQC). Generally, the preferred model is the one with the highest Log Likelihood and the lowest values of AIC, SIC, and HQC. Table 4 below presents the results of the model order selection process.
Among the twenty-four ARMA model specifications estimated, the ARMA(3,3) model exhibits the highest Log Likelihood value (-24.0103) and the lowest AIC (0.2552), SIC (0.3159), and HQC (0.2958) values. These results indicate that the ARMA(3,3) model provides the best balance between goodness-of-fit and parsimony.
Table 4:Model Order Selection using Log Likelihood and Information Criteria
| S/n | Model | LogL | AIC | SIC | HQC |
| 1. | ARMA(0,1) | -34.4597 | 0.2964 | 0.3349 | 0.3079 |
| 2. | ARMA(1,0) | -34.8194 | 0.3006 | 0.3391 | 0.3121 |
| 3. | ARMA(1,1) | -32.9444 | 0.2934 | 0.3363 | 0.3107 |
| 4. | ARMA(0,2) | -34.4107 | 0.3042 | 0.3469 | 0.3214 |
| 5. | ARMA(2,0) | -35.1256 | 0.3125 | 0.3555 | 0.3298 |
| 6. | ARMA(1,2) | -32.9256 | 0.3014 | 0.3586 | 0.3245 |
| 7. | ARMA(2,1) | -33.2988 | 0.3057 | 0.3631 | 0.3288 |
| 8. | ARMA(2,2) | -30.3771 | 0.2899 | 0.3616 | 0.3188 |
| 9. | ARMA(0,3) | -34.4060 | 0.3122 | 0.3692 | 0.3352 |
| 10. | ARMA(3,0) | -35.4688 | 0.3248 | 0.3823 | 0.3480 |
| 11. | ARMA(1,3) | -28.0912 | 0.2701 | 0.3616 | 0.3089 |
| 12. | ARMA(3,1) | -32.9028 | 0.3119 | 0.3838 | 0.3409 |
| 13. | ARMA(2,3) | -30.3708 | 0.2981 | 0.3841 | 0.3328 |
| 14. | ARMA(3,2) | -30.5304 | 0.3007 | 0.3859 | 0.3354 |
| 15. | ARMA(3,3)** | -24.0103 | 0.2552 | 0.3159 | 0.2958 |
| 16. | ARMA(0,4) | -34.1157 | 0.3180 | 0.3893 | 0.3467 |
| 17. | ARMA(4,0) | -35.3492 | 0.3335 | 0.4056 | 0.3625 |
| 18. | ARMA(1,4) | -34.4466 | 0.3302 | 0.4159 | 0.3647 |
| 19. | ARMA(4,1) | -35.3432 | 0.3417 | 0.4282 | 0.3765 |
| 20. | ARMA(2,4) | -32.0099 | 0.3198 | 0.4201 | 0.3602 |
| 21. | ARMA(4,2) | -26.7027 | 0.2785 | 0.3795 | 0.3192 |
| 22. | ARMA(3,4) | -25.4065 | 0.2799 | 0.3899 | 0.3213 |
| 23. | ARMA(4,3) | -33.4797 | 0.3428 | 0.4581 | 0.3893 |
| 24. | ARMA(4,4) | -31.4253 | 0.2962 | 0.4060 | 0.3285 |
Therefore, based on the information criteria, the ARMA(3,3) model is selected as the optimal model for forecasting short-term variations in non–insulin-dependent diabetes cases among farmers in Benue State. This suggests that both autoregressive and moving average components up to the third order significantly contribute to capturing the dynamic structure of the series.
4.6 Parameter Estimates of ARMA(3,3) Model
After selecting the ARMA(3,3) model as the optimal specification based on the information criteria, the model parameters were estimated to evaluate the dynamic relationship between past observations and random disturbances in the series of non–insulin-dependent diabetes cases among farmers in Benue State. Table 5 below presents the estimated coefficients of the ARMA(3,3) model, along with their corresponding standard errors, t-statistics, and p-values. Goodness-of-fit measures such as the R-squared, Adjusted R-squared, F-statistic, and Durbin–Watson statistic are also reported to assess the adequacy of the fitted model.
Table 5: Parameter Estimates of ARMA(3,3) Model
| Variable | Coefficient | Std. Error | t-Statistic | p-value |
| C | 8.768664 | 0.017218 | 509.2761 | 0.0000 |
| AR(1) | 0.366096 | 0.024641 | 14.85713 | 0.0000 |
| AR(2) | 0.311203 | 0.029382 | 10.59171 | 0.0000 |
| AR(3) | -0.912359 | 0.024212 | -37.68166 | 0.0000 |
| MA(1) | -0.372828 | 0.009593 | -38.86277 | 0.0000 |
| MA(2) | -0.386923 | 0.009312 | -41.55086 | 0.0000 |
| MA(3) | 0.982389 | 0.007644 | 128.5160 | 0.0000 |
| R-squared | 0.890511 | AIC | 0.255229 | |
| Adjusted R2 | 0.867389 | SIC | 0.315852 | |
| F-statistic | 6.914400 | HQC | 0.295759 | |
| Prob(F-stat.) | 0.000951 | Durbin-Watson stat. | 2.011502 |
The model estimation results reported in Table 5 show that all autoregressive (AR) and moving average (MA) coefficients are statistically significant at the 1% level, as indicated by their very low p-values (p < 0.01). This implies that past values and past error terms up to the third lag significantly influence the current level of non–insulin-dependent diabetes cases among farmers.
Specifically, the positive coefficients of AR(1) and AR(2) suggest a direct persistence effect, meaning that increases in diabetes cases in the immediate past periods tend to raise current cases. Conversely, the negative AR(3) coefficient indicates a corrective mechanism, implying that after about three periods, the series tends to revert toward its mean. The MA terms also show alternating positive and negative signs, suggesting that short-term shocks have both dampening and amplifying effects over time before dissipating.
The high R-squared (0.8905) and adjusted R-squared (0.8674) values indicate that approximately 89% of the variation in diabetes cases is explained by the model, signifying a very good fit. The F-statistic (6.9144) with a significant probability value (0.000951) confirms the overall significance of the model.The Durbin–Watson statistic (2.0115) is close to 2, suggesting the absence of serial correlation in the residuals, while the information criteria (AIC = 0.2552, SIC = 0.3159, HQC = 0.2958) reaffirm that the ARMA(3,3) model remains the most parsimonious and efficient choice.
Overall, the ARMA(3,3) model adequately captures the temporal dynamics and short-term fluctuations in non–insulin-dependent diabetes cases among farmers in Benue State, making it suitable for reliable short-term forecasting.
4.7 Model Diagnostic Checks
Following the estimation of the ARMA(3,3) model for predicting non–insulin-dependent diabetes cases among farmers in Benue State, diagnostic checks such as multicolinearity test and Ljung-Box Q-statistic tests were conducted to verify the adequacy of the fitted model. This assessment ensures that the residuals behave like white noise, uncorrelated, homoscedastic, and pattern-free over time. The test are presented in the following subsections.
4.7.1 Multicolinearity test result
Multicollinearity diagnostics were performed to make sure the variables in ARMA(3,3) model weren’t overlapping too much. Using the Variance Inflation Factor (VIF) for each autoregressive (AR) and moving average (MA) term, the test assessed how multicollinearity might affect the stability and reliability of parameter estimates. Generally, VIF values above 10 indicate severe multicollinearity, values between 5 and 10 suggest moderate correlation, and values below 5 imply no serious concern. The results presented in Table 6 show both uncentered and centered VIF statistics for the ARMA(3,3) model parameters.
The results of multicolinearity test reported in Table 6 below reveal that all centered VIF values are considerably low, ranging between 1.11 and 2.55, which are far below the critical threshold of 10. This indicates that there is no serious multicollinearity among the explanatory variables (AR and MA terms) in the estimated ARMA(3,3) model.
Therefore, the estimated parameters are statistically reliable, and the standard errors are not inflated by multicollinearity. This implies that the ARMA (3,3) model is well-conditioned, and the coefficients can be interpreted with confidence.
Table 6: Test for Multicolinearity (Variance Inflation Factors)
| Coefficient | Uncentered | Centered | |
| Variable | Variance | VIF | VIF |
| C | 0.000296 | 1.018813 | Na |
| AR(1) | 0.000607 | 1.779456 | 1.779044 |
| AR(2) | 0.000863 | 2.552345 | 2.552344 |
| AR(3) | 0.000586 | 1.768375 | 1.768101 |
| MA(1) | 9.20E-05 | 1.257613 | 1.255458 |
| MA(2) | 8.67E-05 | 1.213557 | 1.203709 |
| MA(3) | 5.84E-05 | 1.121942 | 1.111356 |
4.7.2 Ljung-Box Q-statistic test result for serial correlation
The Autocorrelation Function (ACF), Partial Autocorrelation Function (PACF), and Ljung–Box Q-statistics were used to test for serial correlation. High p-values (greater than 0.05) for the Q-statistics indicate no significant autocorrelation, suggesting that the residuals are random and the model is well specified. Table 5 presents these diagnostic test results for the ARMA(3,3) model residuals.
The results of Q-statistic reported in Table 5 and the ACF as well as PACF plots reported in Figure 4 show that all residual autocorrelations (ACF and PACF) are very small and fluctuate closely around zero across all 36 lags. None of the autocorrelation coefficients appear significant, suggesting that the residuals from the ARMA(3,3) model are approximately white noise.
Furthermore, the Ljung–Box Q-statistics have p-values consistently greater than 0.05, indicating that the null hypothesis of no autocorrelation cannot be rejected at any lag. This confirms that there is no statistically significant serial correlation remaining in the residuals. In addition, the Durbin–Watson statistic from the model estimation (2.0115) supports this conclusion by indicating near-zero autocorrelation in the residuals.
Overall, these diagnostic results confirm that the ARMA(3,3) model is well specified, the residuals are independently and randomly distributed, and the model provides a statistically adequate fit to the data. Therefore, the model is suitable for reliable short-term forecasting of non–insulin-dependent diabetes cases among farmers in Benue State
Table 7: Autocorrelations and Ljung-Box Q-Statistic Test Results of Residuals
| Lag | ACF | PACF | Q-Statistics | p-value |
| 1 | -0.024 | -0.024 | 0.1415 | 0.707 |
| 2 | -0.012 | -0.012 | 0.1760 | 0.916 |
| 3 | -0.069 | -0.070 | 1.3558 | 0.716 |
| 4 | 0.007 | 0.003 | 1.3669 | 0.850 |
| 5 | -0.126 | -0.128 | 5.3247 | 0.378 |
| 6 | -0.036 | -0.048 | 5.6541 | 0.463 |
| 7 | -0.017 | -0.024 | 5.7294 | 0.572 |
| 8 | 0.142 | 0.124 | 10.812 | 0.213 |
| 9 | -0.042 | -0.042 | 11.254 | 0.259 |
| 10 | 0.046 | 0.032 | 11.802 | 0.299 |
| 11 | -0.021 | -0.015 | 11.918 | 0.370 |
| 12 | 0.052 | 0.044 | 12.628 | 0.397 |
| 13 | -0.025 | 0.012 | 12.794 | 0.464 |
| 14 | -0.009 | -0.008 | 12.815 | 0.541 |
| 15 | 0.062 | 0.080 | 13.804 | 0.540 |
| 16 | 0.068 | 0.053 | 15.019 | 0.523 |
| 17 | 0.112 | 0.147 | 18.316 | 0.369 |
| 18 | 0.109 | 0.127 | 21.475 | 0.256 |
| 19 | -0.008 | 0.027 | 21.493 | 0.310 |
| 20 | -0.087 | -0.066 | 23.529 | 0.264 |
| 21 | -0.066 | -0.032 | 24.707 | 0.260 |
| 22 | -0.020 | 0.010 | 24.810 | 0.306 |
| 23 | -0.062 | -0.057 | 25.855 | 0.308 |
| 24 | -0.048 | -0.064 | 26.480 | 0.329 |
| 25 | 0.021 | -0.044 | 26.599 | 0.376 |
| 26 | 0.020 | -0.037 | 26.704 | 0.425 |
| 27 | -0.033 | -0.069 | 27.003 | 0.464 |
| 28 | 0.065 | 0.050 | 28.156 | 0.456 |
| 29 | 0.052 | 0.030 | 28.898 | 0.470 |
| 30 | 0.062 | 0.046 | 29.969 | 0.467 |
| 31 | 0.014 | 0.040 | 30.023 | 0.516 |
| 32 | 0.010 | 0.016 | 30.053 | 0.565 |
| 33 | 0.042 | 0.050 | 30.555 | 0.589 |
| 34 | 0.003 | 0.004 | 30.558 | 0.637 |
| 35 | -0.039 | -0.013 | 30.994 | 0.662 |
| 36 | -0.008 | -0.001 | 31.014 | 0.705 |
Figure 4:Plot of Correlogram of Residuals of Estimated ARMA(3,3) Model
4.8 Forecast and Forecast Evaluation
To evaluate the predictive performance of the ARMA(3,3) model in forecasting non–insulin-dependent diabetes cases among farmers in Benue State, forecast accuracy measures were computed. The Root Mean Squared Error (RMSE), Mean Absolute Error (MAE), and Mean Absolute Percentage Error (MAPE) were used to assess both in-sample and out-of-sample forecast accuracy. Lower values of these statistics indicate better model performance and predictive reliability. The result is presented in Table 8.
The results of forecast comparison reported in Table 8below show that the out-of-sample forecast achieved slightly lower RMSE (0.2671), MAE (0.2310), and MAPE (2.6490) values compared to the in-sample forecast (RMSE = 0.2715, MAE = 0.2446, MAPE = 2.6781). This suggests that the ARMA(3,3) model demonstrates strong predictive capability, with minimal forecast error and good generalization performance. The model selected in forecast mode, as denoted by the accuracy measures, provides reliable short-term out-of-sample predictions of non–insulin-dependent diabetes cases.
Table 8: Forecast Comparison using Accuracy Measures
| RMSE | MAE | MAPE | |
| In-Sample | 0.271510 | 0.244615 | 2.678116 |
| Out-of-Sample** | 0.267100 | 0.231048 | 2.649005 |
Note: ** denotes forecast mode selected by accuracy measures.
4.8.1 Forecast of Diabetes Miletus in Benue State from July, 2025 to June, 2027
To evaluate the short-term predictive performance of the ARMA(3,3) model, forecasts of non–insulin-dependent diabetes (Type-2 Diabetes Mellitus) cases among farmers in Benue State were generated for the period July 2025 to June 2027. The forecasts were computed in natural logarithmic form and then converted to actual population estimates. For each forecast, the standard error, lower confidence limit (LCL), and upper confidence limit (UCL) were calculated at a 95% confidence level, using 
Table 9: “Forecast of Diabetes Miletus Infection Cases in Benue State from July 2025-
June, 2027″
| Year: Month | Forecast (natural log form) | Actual Forecast (No. of Persons) | |||
| Forecast | Std. error | LCL | Forecast | UCL | |
| 2025:06 | 6.9967 | — | — | 8896 | — |
| 2025:07 | 8.77405 | 0.271243 | 3799 | 6464 | 11000 |
| 2025:08 | 8.72655 | 0.271669 | 3619 | 6165 | 10499 |
| 2025:09 | 8.78204 | 0.271670 | 3826 | 6516 | 11098 |
| 2025:10 | 8.77132 | 0.272065 | 3782 | 6447 | 10988 |
| 2025:11 | 8.80141 | 0.272672 | 3893 | 6644 | 11337 |
| 2025:12 | 8.74519 | 0.272672 | 3680 | 6281 | 10717 |
| 2026:01 | 8.76088 | 0.272790 | 3738 | 6380 | 10889 |
| 2026:02 | 8.74585 | 0.273455 | 3677 | 6285 | 10741 |
| 2026:03 | 8.79725 | 0.273466 | 3871 | 6616 | 11308 |
| 2026:04 | 8.77366 | 0.273476 | 3781 | 6462 | 11044 |
| 2026:05 | 8.77825 | 0.274040 | 3794 | 6492 | 11107 |
| 2026:06 | 8.73648 | 0.274110 | 3638 | 6226 | 10654 |
| 2026:07 | 8.76803 | 0.274114 | 3755 | 6426 | 10996 |
| 2026:08 | 8.76810 | 0.274473 | 3752 | 6426 | 11005 |
| 2026:09 | 8.79729 | 0.274652 | 3862 | 6616 | 11335 |
| 2026:10 | 8.76026 | 0.274669 | 3722 | 6376 | 10923 |
| 2026:11 | 8.76113 | 0.274824 | 3724 | 6381 | 10936 |
| 2026:12 | 8.74504 | 0.275111 | 3662 | 6279 | 10767 |
| 2027:01 | 8.78341 | 0.275121 | 3805 | 6525 | 11188 |
| 2027:02 | 8.77734 | 0.275152 | 3782 | 6486 | 11121 |
| 2027:03 | 8.78223 | 0.275481 | 3798 | 6517 | 11183 |
| 2027:04 | 8.74716 | 0.275481 | 3667 | 6293 | 10798 |
| 2027:05 | 8.76058 | 0.275481 | 3717 | 6378 | 10944 |
| 2027:06 | 8.76313 | 0.275759 | 3724 | 6394 | 10978 |
| Total | 210.40663 | 154075 | |||
| Average | 8.766942917 | 6419.7917 | |||
Note: For 95% confidence intervals, 
Figure 5: Forecast Graph of Diabetes Miletus in Benue State from July, 2025-June, 2027
The forecast results reported in Table 9 and Figure 5 above reveals that the predicted number of non–insulin-dependent diabetes cases among farmers in Benue State is expected to fluctuate moderately over the two-year forecast horizon (July 2025–June 2027). The monthly forecasts range between approximately 3,600 and 11,300 cases, with an overall average of about 6,420 cases per month and a total forecast of 154,075 cases during the study period. The relatively narrow confidence intervals across months suggest a high level of precision in the model’s predictions.
Overall, the ARMA(3,3) model demonstrates strong forecasting capability, indicating that diabetes prevalence among farmers in Benue State is likely to remain fairly stable with mild month-to-month variations over the forecast period.
4.9 Implications of the Study to Farmers and Postharvest Losses in Benue State
The implications of this study for farmers and postharvest losses in Benue State are significant from both public health and socio-economic perspectives. The findings, which forecast the prevalence of non–insulin-dependent diabetes (Type-2 Diabetes Mellitus) among farmers, suggest that a substantial portion of the agricultural workforce may experience declining health and productivity over time. Poor health conditions such as diabetes can reduce farmers’ physical capacity to engage in strenuous agricultural activities, particularly during critical periods like harvesting and processing. “This in turn increases the likelihood of postharvest losses, as crops may remain un-harvested or inadequately stored due to reduced labour efficiency and absenteeism resulting from illness”.
Moreover, “higher diabetes prevalence among farmers implies increased medical expenditures and a diversion of household income away from agricultural investment”, further compounding the problem of low productivity and waste. The study underscores the urgent need for integrated health and agricultural policies—including improved rural healthcare services, regular medical screening, health education on diet and lifestyle, and the promotion of labour-saving technologies—to mitigate the dual burden of disease and postharvest losses. Ultimately, addressing the health challenges of farmers is crucial for achieving food security, sustaining agricultural livelihoods, and enhancing overall economic resilience in Benue State.
4.0 Conclusion
The study demonstrates that the ARMA(3,3) model effectively forecasts the incidence of non-insulin-dependent diabetes among farmers in Benue State, Nigeria, The analysis revealed that the ARMA(3,3) model provided the best fit based on information criteria and diagnostic tests, with residuals behaving like white noise, indicating a well-specified and reliable model. The forecasts from July 2025 to June 2027 suggest a steady and relatively high incidence of diabetes cases among farmers, implying that the disease poses an ongoing public health concern within the agricultural population. This condition could adversely affect farmers’ productivity, increase medical costs, and indirectly contribute to higher postharvest losses due to reduced labour availability and inefficiencies in farm management. These findings highlight the interconnectedness between health and agricultural output, emphasizing that the burden of chronic diseases like diabetes extends beyond healthcare into the realm of food security and economic stability. Therefore, proactive health interventions and policy integration between the health and agricultural sectors are vital. Ensuring farmers’ wellness through preventive care, early detection, and education can significantly reduce the impact of diabetes and its broader economic consequences. The study provides empirical evidence to guide policymakers, healthcare providers, and agricultural development agencies in formulating context-specific strategies to improve both health outcomes and agricultural sustainability in Benue State.
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