The study utilizes annual time series data for total cereal production (measured in tons) in Somalia from 1961 to 2023, sourced from Word Bank.

Figure 1 visualizes the annual cereal production rate in Somalia from 1962 to 2023, effectively plotting the sector’s volatile trajectory and highlighting the non-stationary nature of the time series. The graph reveals a dramatic “broken trend” structure: it begins with a baseline of relative stability during the 1960s and 1970s, followed by a sharp, linear ascent in the 1980s where production reached historical peaks. However, this growth is abruptly severed by a precipitous vertical drop in the early 1990s, representing the structural collapse of the agricultural system. The latter half of the timeline (1996-2023) is characterized by high-frequency oscillations, where the curve swings violently between transient recoveries and deep production troughs. This visual pattern underscores the paper’s core premise: that Somali cereal production is no longer defined by a consistent trend, but rather by stochastic shocks that challenge traditional linear forecasting methods. Abdi et al. (2024) attribute the inability to sustain the high production rates seen in the 1980s to the diminishing resilience of major Somali crops against intensifying climate variability, which locks the country into the volatile pattern seen in the graph’s recent years [1]. The specific “deep troughs” visible in the 2000s and 2010s are contextualized by Anderson et al. (2023), who link these sharp declines to the increasing frequency of multi-season droughts driven by La Niña events, which systematically disrupt the region’s bimodal rainfall patterns [24]. Furthermore, Warsame et al. (2023) argue that the stagnation observed after the 1990 structural break is compounded by the “conflict environment nexus”, where political instability and environmental degradation prevent the agricultural sector from recovering its historical potential [40]. Consequently, Funk et al. (2023) emphasize that this extreme variability necessitates a move away from static planning toward dynamic, proactive forecasting systems capable of predicting such climatic extremes [34].

Figure 1. Cereal crop production in Somalia 1962-2023 (source: World Bank [56]).

Table 1 provides a comprehensive statistical profile of Somali cereal production over the 63-year study period (1961-2023), revealing a dataset defined by extreme instability and high dispersion. The mean annual production stands at 295,138 tons, yet this figure is overshadowed by a substantial standard deviation of 118,949 tons, indicating that actual yields fluctuate wildly from the average. The dataset exhibits a massive range of 542,707 tons, stretching from a minimum of 111,052 tons to a historical maximum of 653,760 tons. Abdi et al. (2024) attribute this statistical dispersion to the low resilience of Somali crops against increasingly erratic climate patterns, which creates the wide “yield gaps” evident in the range between minimum and maximum output [1].

Table 1.Descriptive statistics and distribution characteristics of cereal production in Somalia (1961-2023) (source: World Bank [56]).

The significant standard deviation mirrors findings by Öztürk and Türkyılmaz (2024), who note that such statistical volatility is characteristic of non-stationary agricultural time series, necessitating the use of non-linear modeling over simple averages to capture the true nature of the data [6]. Furthermore, Zhao (2024) emphasizes that these fluctuations are not merely weather-related but are exacerbated by socioeconomic vulnerabilities, which drag the mean production levels down despite potential capacity [7]. Finally, Warsame et al. (2023) provide context for the positive skew (prevalence of lower values), arguing that the “conflict-environment nexus” has degraded the agricultural baseline, locking production figures into the lower quantiles observed in the dataset [40].

The stationarity of the time series was examined using the Augmented Dickey Fuller (ADF), Phillips-Perron (PP), and Kwiatkowski-Phillips-Schmidt-Shin (KPSS) tests. At the level form, the results were mixed; while the KPSS test failed to reject stationarity, both the ADF (t = −2.7014, p = 0.2909, t = −2.7014, p = 0.2909) and PP (t = −17.916, p = 0.0845, t = −17.916, p = 0.0845) tests failed to reject the null hypothesis of a unit root at the 5% significance level, suggesting the presence of non-stationarity.

The first-differenced results showed strong evidence of stationarity across all three tests. The ADF (t = −5.2255, t = −5.2255) and PP (t = −74.915, t = −74.915) tests yielded p-values less than 0.01, rejecting the null hypothesis of a unit root at the 1% level.

Table 2 outlines the ten-year predictive horizon for Somali cereal production (2024-2033) utilizing the NNETAR model, which was identified as the most robust forecasting tool in the study. The data projects a trajectory of slow, oscillating recovery, with point forecasts estimating an increase in production from 210,380.1 tons in 2024 to 285,849.6 tons by 2033. While the mean forecast suggests a gradual stabilization of domestic output following historical volatility, the confidence intervals reveal a persistent underlying risk; specifically, the 95% confidence interval remains extremely wide, ranging from a low of 52,554 tons to a high of 519,144 tons in 2033. This substantial divergence between the upper and lower bounds underscores the agricultural sector’s continued vulnerability to external shocks, suggesting that while a baseline recovery is anticipated, the potential for severe production deficits remains statistically significant without structural interventions. The projected volatility and the demonstrated superiority of non-linear modeling in this study align closely with recent empirical findings regarding food security in the Horn of Africa. Abdi et al. (2024) corroborate our findings on production vulnerability, noting that despite adaptive strategies, Somali staple crops remain highly sensitive to climate variability, which necessitates the type of robust uncertainty modeling presented in our confidence intervals [1]. Furthermore, the shift towards computational intelligence advocated in our results is supported by Öztürk and Türkyılmaz (2024), whose comparative analysis confirmed that Neural Network models significantly outperform traditional ARIMA frameworks in forecasting agricultural commodities characterized by non-linear trends [6]. Contextualizing the food security implications, Zhao (2024) emphasizes that accurate prediction in Somalia is now a critical component of humanitarian strategy, reinforcing our conclusion that simple linear trends are insufficient for policy planning [7]. Finally, Sancar (2024) argues that the transition to “Smart Agriculture” relies on such predictive analytics to manage the risks inherent in modern food production systems [12].

Table 2.Ten years forecast of the cereal production in Somalia (source: World Bank [56]).

Table 3 presents a rigorous comparative evaluation of eight distinct forecasting models applied to the unseen test dataset spanning 2014 to 2023. The empirical results establish a clear hierarchy in predictive performance, with the Neural Network Autoregressive (NNETAR) model demonstrating superior accuracy across all key metrics. NNETAR achieved the lowest Root Mean Square Error (RMSE) of 95,426.9 and a Symmetric Mean Absolute Percentage Error (SMAPE) of 40.42%, indicating its robust capacity to handle the non-linear dynamics of Somali cereal production. In contrast, traditional statistical benchmarks faltered; the Exponential Smoothing (ETS) model followed with a significantly higher SMAPE of 54.94%, while the widely used ARIMA and Theta models performed poorly, with error rates exceeding 57% and 68% respectively. Crucially, the table reveals a systemic negative bias across all models—indicated by negative Mean Error (ME) values (e.g., NNETAR at −87,360.80)—suggesting a general tendency to over-forecast production levels during the severe drought conditions that characterized the validation period. The findings presented in Table 4, specifically the performance gap between computational intelligence and linear models, are strongly corroborated by recent literature in agricultural forecasting. Öztürk and Türkyılmaz (2024) support this study’s methodological conclusion, reporting that Artificial Neural Networks (ANN) and LSTM models consistently outperform ARIMA in capturing the volatility of agricultural commodity prices [6]. Similarly, Ahmar et al. (2023) conducted a comparative analysis of food grain prediction, concluding that Neural Network Autoregressive (NNAR) models provide significantly higher accuracy than Holt-Winters and ARIMA approaches when dealing with complex time series data [4]. The operational necessity of adopting these advanced analytics is emphasized by Sancar (2024), who argues that the transition to “Smart Agriculture” requires moving beyond descriptive statistics to precision modeling to mitigate production risks [12]. Furthermore, Abdi et al. (2024) reinforce the contextual importance of these findings for Somalia, noting that advanced modeling is essential to understand crop resilience against the specific climate change implications threatening the region’s food security [1].

Table 3.Comparative accuracy of forecasting models on the test set (2014-2023) (source: World Bank [56]).

3.5.1. Analysis of Model Performance

The Neural Network Autoregressive (NNETAR) model demonstrated superior accuracy across all error metrics, establishing itself as the most robust tool for forecasting cereal production in this specific context. It achieved the lowest Root Mean Square Error (RMSE) of 95,426.9 and a Symmetric Mean Absolute Percentage Error (SMAPE) of 40.42%, significantly outperforming traditional linear benchmarks.

Following the NNETAR model, the Exponential Smoothing (ETS) framework emerged as the second-most effective approach, recording a SMAPE of 54.94%. The performance of the ARFIMA and ARIMA models was largely comparable, forming a middle tier of accuracy with SMAPE values of approximately 57.6%. Conversely, the BATS, TBATS, and Theta models exhibited substantially higher error rates, rendering them less suitable for this dataset. A critical observation from the Mean Error (ME) and Mean Percentage Error (MPE) metrics is the consistent negativity across all models. This trend indicates a systemic bias toward over forecasting; the models generally predicted higher production levels than were actually realized during the test period. This systematic error likely reflects the models’ struggle to fully account for the sharp downturns in yield associated with the severe drought conditions and structural breaks characteristic of the 2014-2023 validation period.

3.5.2. Forecasting Models

Eight distinct time series forecasting models were implemented and compared.

1.ARIMA (Autoregressive Integrated Moving Average): A widely used class of models that explains a time series based on its own past values, its own past errors, and a differencing process to achieve stationarity. The model is denoted as ARIMA(p,d,q), where “p” is the order of the autoregressive component, “d” is the degree of differencing, and “q” is the order of the moving average component [57]. We employed the auto.arima function, which automatically selects the optimal p, d, and q parameters based on information criteria (e.g., AIC).

2.ETS (Error, Trend, Seasonality): Also known as exponential smoothing state-space models, ETS models capture the underlying structure of a time series through three components: error, trend (additive or multiplicative), and seasonality (additive or multiplicative). The algorithm automatically selects the best-fitting model from a suite of possibilities [58].

3.BATS and TBATS: These are extensions of ETS models designed to handle complex seasonal patterns, such as multiple seasonalities or non-integer seasonality. TBATS uses Box-Cox transformation (T), ARMA errors (A), Trend (T), and Seasonal (S) components.

4.Theta Model: A simple but effective forecasting method that decomposes a time series into two “theta lines”. The final forecast is a combination of the extrapolation of these two lines. It has proven to be remarkably robust, especially for longer forecast horizons.

5.ARFIMA (Autoregressive Fractionally Integrated Moving Average): An extension of the ARIMA model that allows for a fractional differencing parameter, making it particularly useful for modelling long-memory processes, where dependencies between distant observations decay more slowly than in short-memory processes.

6.NNETAR (Neural Network Autoregressive Model): This model uses a feed-forward neural network to model a time series, where past values of the series are used as inputs to forecast future values. This allows the model to capture complex non-linear relationships in the data that linear models like ARIMA cannot [3].

7.ANN (Artificial Neural Network): A Multi-Layer Perceptron (MLP) from the ANN package was used. This is another form of neural network specifically adapted for time series forecasting, which involves preprocessing, scaling, and iterative forecasting using hidden neuron layers to model complex patterns.

3.5.3. Model Evaluation

The accuracy of each model was evaluated by comparing its 10-year forecast against the actual values in the test set. Four standard error metrics were calculated:

Mean Absolute Error (MAE): The average of the absolute differences between the predicted and actual values.Root Mean Squared Error (RMSE): The square root of the average of the squared differences, which penalizes larger errors more heavily.Mean Absolute Percentage Error (MAPE): Measures the average percentage error, providing a relative sense of error size.Symmetric Mean Absolute Percentage Error (SMAPE): A modified version of MAPE.

That is less biased when actual values are close to zero and has both lower and upper bounds. The model with the consistently lowest values across these metrics on the test set was identified as the most accurate and robust for this dataset.

3.5.4. Model Fitting

Table 4details the statistical diagnostics and parameter estimates for the optimal ARIMA model derived during the training phase (1961-2013). Using the auto.arima selection algorithm based on information criteria, the study identified an ARIMA (1,0,0) structure with a non-zero mean as the best-fitting linear model. The table reports a Log Likelihood of −802.97, along with an Akaike Information Criterion (AIC) of 1611.93 and a Bayesian Information Criterion (BIC) of 1618.36. These metrics serve as indicators of the model’s goodness-of-fit relative to its complexity, suggesting that while the First-Order Autoregressive term successfully captured the immediate linear dependencies, the extremely high Sigma squared (σ2σ2) value of 7.04 × 1097.04 × 109 highlights the massive residual variance. This substantial variance reflects the model’s struggle to fully encompass the extreme volatility and structural breaks inherent in the Somali cereal production dataset without the aid of non-linear components. The methodological challenges and findings illustrated in Table 4 align with recent literature regarding the fitting of time series models to volatile agricultural data. The use of AIC and BIC for model selection, as employed here, is validated by Majhi et al. (2023), who emphasize that these criteria are essential for balancing model parsimony against accuracy when predicting food price indices and production volumes [10]. However, the high variance (σ2σ2) noted in your ARIMA results is consistent with the findings of Öztürk and Türkyılmaz (2024), whose comparative study demonstrates that while ARIMA provides a necessary statistical baseline, it frequently exhibits higher error variances compared to AI-driven models when applied to non-stationary agricultural commodities [6]. Furthermore, Ahmar et al. (2023) report similar results in India, observing that while ARIMA models are theoretically robust, they often fail to capture the complex, non-linear patterns of food grain production as effectively as Neural Network Autoregressive (NNAR) approaches [4]. Finally, the underlying reasons for the high volatility captured by your model’s parameters are contextualized by Abdi et al. (2024), who argue that the resilience of major crops in Somalia is continuously tested by climate change, necessitating the move toward more adaptive modeling techniques illustrated in your broader study [1].

Table 4. Series: cereal, ARIMA(1,0,0) with non-zero mean (source: World Bank [56]).

3.5.5. ARIMA(1,0,0) with Non-Zero Measure

The auto.arima procedure selected an ARIMA(1,0,0) with a non-zero mean as the best ARIMA model. The Ljung-Box test performed on the model’s residuals yielded a p-value of 0.47, indicating that the residuals were independently distributed (i.e., like white noise), thus confirming the model’s adequacy. The diagnostic plots for the ARIMA model are shown in Figure 2. The best ETS model selected was an ETS(M,N,N), indicating a model with multiplicative error, no trend, and no seasonality. The NNETAR model was configured as an NNAR(3,1,2), signifying a network with 3 lagged inputs, 1 hidden layer with 2 nodes, and 20 repetitions to average the results.

Figure 2.Residual diagnostics for the ARIMA(1,0,0) model (source: World Bank [56]).

3.5.6. Residual Diagnostics for the ARIMA(1,0,0) Model

Figure 2 illustrates the residual diagnostics for the ARIMA(1,0,0) model, serving as a critical visual validation of the linear model’s statistical adequacy. The top panel plots the residuals over time, revealing significant variance that mirrors the high volatility periods identified in the historical dataset. The Autocorrelation Function (ACF) plot in the bottom left is particularly significant; it shows that all autocorrelation bars fall within the blue dashed significance limits, confirming that there is no remaining temporal dependence in the error terms—effectively rendering them “white noise”. This visual evidence supports the study’s Ljung-Box test result (p = 0.47), indicating that while the ARIMA model successfully extracted the linear correlations from the series, the large residuals shown in the histogram (bottom right) reflect the model’s inability to fully capture the magnitude of the non-linear shocks compared to the neural network models.

The finding that an ARIMA model can be statistically valid (passing diagnostic checks) yet underperform in predictive accuracy compared to AI models is well-supported by recent agricultural forecasting literature. Öztürk and Türkyılmaz (2024) corroborate this, noting that while ARIMA models frequently pass residual diagnostic tests like the ACF, they often fail to capture the structural non-linearities in volatile agricultural markets as effectively as LSTM or ANN models [6]. Ahmar et al. (2023) reinforce this distinction, demonstrating in their study of food grains that while ARIMA serves as a robust benchmark with stable residuals, Neural Network Autoregressive (NNAR) models consistently provide superior accuracy in complex biological systems [4]. The necessity of these diagnostic evaluations is emphasized by Majhi et al. (2023), who argue that analyzing ACF plots and residual distributions is a prerequisite for validating any time series model applied to cereal price or production indices [10]. Furthermore, the high variance observed in the residual time plot is contextually explained by Abdi et al. (2024), who attribute such erratic deviations in Somali crop data to the specific lack of resilience against intensifying climate change impacts [1].

3.5.7. Comparative Forecast Accuracy

Figure 3 presents a multi-panel visual comparison of the eight forecasting models evaluated in the study, plotting their predicted trajectories against the historical cereal production data of Somalia. The visualization reveals a stark contrast in behavioral dynamics between linear and non-linear approaches. The panels for traditional models, such as ARIMA and Theta, display relatively rigid, linear trend extrapolations with rapidly expanding shaded confidence intervals, indicating a high degree of uncertainty and an inability to capture short-term fluctuations. Conversely, the computational intelligence models, specifically the Neural Network Autoregressive (NNETAR) and ANN, exhibit distinct non-linear patterns that attempt to adapt to the historical volatility. This visual assessment reinforces the empirical error metrics (Table 4), highlighting that while linear models tend to “smooth out” the data—thereby missing critical structural breaks—the neural

Figure 3. Visual comparison of the forecasts generated by each of the eight models against the historical data (Source: World Bank [56]).

networks provide a more complex projection that better reflects the stochastic nature of the country’s rainfall-dependent agriculture. The visual divergence between the static linear forecasts and the adaptive AI-driven projections shown in Figure 4 is consistent with recent findings in agricultural data science. Öztürk and Türkyılmaz (2024) observed similar visual trends in their comparative study, noting that while ARIMA models produce smooth, mean-reverting forecasts, they visually fail to track the abrupt structural breaks in commodity prices compared to LSTM or Neural Networks [6]. Ahmar et al. (2023) reinforce this observation, demonstrating that in comparative plots of food grain data, NNAR models provide a tighter fit to historical oscillations than Holt-Winters or ARIMA, which often fail to react to sudden shifts in the data generating process [4]. The operational necessity of adopting these more complex visual models is contextualized by Sancar (2024), who argues that the “Third Green Revolution” demands moving beyond static descriptive statistics toward dynamic AI models capable of supporting precision agriculture [12]. Finally, the wide confidence intervals observed in Figure 4 are explained by Abdi et al. (2024), who attribute the high unpredictability of the data to the specific lack of climate resilience in Somali staple crops [1].

Figure 4.Arnn forecast (Source: World Bank [56]).

3.5.8. Forecast Projections

Forecasted Values (2024-2033) from NNETAR Model:

2024: 240,691 tons;2025: 243,517 tons;2026: 243,782 tons;2027-2033: ~243,810 tons.

Figure 4 visualizes the ten-year forecast for Somali cereal production (2024-2033) generated by the Neural Network Autoregressive (NNETAR) model, which was identified as the study’s superior forecasting instrument. The graph displays the volatile historical time series followed by a projected trajectory that stabilizes relatively quickly compared to the erratic past data. The forecast predicts a slow, oscillating recovery, with production estimated to rise marginally from 240,691 tons in 2024 to approximately 243,810 tons by 2033. This stabilization pattern is characteristic of neural networks trained on data lacking a persistent linear trend; it suggests that without significant structural or technological interventions, domestic production will plateau, failing to return to the peak levels observed in the 1980s. The graph effectively serves as an early warning signal, indicating that the status quo will likely result in stagnation rather than robust growth.

The predictive behavior and the methodological validity of the NNETAR model shown in Figure 4 are strongly supported by recent literature in agricultural data science. Öztürk and Türkyılmaz (2024) corroborate the utility of this approach, finding that Neural Networks consistently outperform linear models like ARIMA in handling the non-linear dynamics of agricultural commodities, although they note that such models often project stability in the absence of strong trend signals [6]. The projected stagnation in production volume is contextually explained by Abdi et al. (2024), who attribute the inability of Somali crops to bounce back to historical highs to a fundamental lack of climate resilience [1]. Furthermore, the operational necessity of using such AI-driven forecasts for planning is highlighted by Sancar (2024), who frames predictive analytics as a key component of “Smart Agriculture” needed to secure food systems in developing nations [12]. Finally, Funk et al. (2023) emphasize that implementing these tailored forecasts is critical for East Africa to move from reactive crisis management to proactive climate adaptation [34].

The plot shows the historical data series followed by the 10-year point forecast from the best performing NNETAR model, which stabilizes quickly. This pattern is characteristic of neural network models trained on data without a strong, persistent trend.