The Gross Domestic Product (GDP) is an economic indicator that reflects the full market value of all final goods and services produced within a country over a certain timeframe, which is typically one year. This value is calculated by combining the monetary worth of these goods and services, resulting in the GDP. There are several techniques that exist for calculating GDP, which include the value-added method and expenditure methods. As it is known that GDP is one of the key economic indicators, it illustrates the state of economic activities and serves as a means to assess economic performance. 

Additionally, it aids in forecasting other indicators like inflation and unemployment (Carter Hill R., et al., 2011; Islam and Alam, 2019; S. Dutta, 2022). GDP analysis is used to reveal the African continent's wide economic potential, marked by performance variety in its 54 countries. Some African economies are always classified among the fastest despite the challenges of political infrastructure, political instability in certain regions, and weakness of external shocks (International Monetary Fund, 2023). However, GDP figures do not reflect the real picture of economic welfare. 

In an effort to examine the GDP of African countries representing geographical, demographic, and economic diversity, the focus was placed on certain African countries that recorded the highest GDP in recent years and are considered the most politically stable and supportive of foreign investment. Understanding and studying the GDP of these countries can provide valuable insights of local economies and economic trends thereby, supporting sustainable economic development. Ethiopia is one of the fastest-growing economies in Africa, with a large population and a strategic geographic location. Egypt, with its diverse economy, holds a pivotal position in the Middle East and Africa, coupled with a substantial population. South Africa stands as one of Africa's largest economies, strategically located at the continent's southern tip. Kenya serves as a key economic hub in East Africa, characterized by a sizable population and significant geographic importance. Thus, the countries under this study represent the geographical diversity spanning from North to South Africa, showcasing significant economic diversity. They exhibit notable economic growth, making them a focal point for investors and economists. Their strategic geographic location in Africa makes them crucial for regional trade and investment. They constitute important consumer markets for products and services, as they characterise with large populations.  These countries also enjoy relative political stability, creating a conducive environment for investment and economic development.

There are some important studies in GDP such as “Trade globalization, green taxation and CO₂ reduction in sub-Saharan Africa”, this study explored trade globalization interrelation, green imposition, and GDP. The item underlies economic unfairness with global systems while on the other hand, rewarding green fixed policies that can sustain long-term sustainability. The research suggested that the green and commercial tax policies can significantly affect GDP performance, especially in the context of economic and environmental reforms. It also revealed that the economies of sub-Saharan Africa are still developing strong mechanisms and climate of weather, but incur useless of envelopes of environmental costs (Omodero, 2019). “The impact of financial development and trade openness on economic growth in emerging markets”, this research examined the impact of financial development and trade liberalization on GDP growth in 19 emerging economies that are primarily located in Asia and Africa. By using dynamic panel data analysis spanning 1990-2016, the study found that both financial development and trade openness significantly boost GDP growth, and therefore it supported the notion that strong financial systems and open trade policies are key drivers of sustainable economic growth in developing countries (Sahoo, et al., 2019). “Forecasting the GDP in the United States by Using ARIMA Model”, this study used the Autoregressive Integrated Moving Average (ARIMA) model to predict the growth of Gross Domestic Product (GDP) in the United States. The analysis covered 93 years of GDP data (1929-2022), and it concluded that the ARIMA (1,1,1) model is a reliable tool for predicting GDP growth in the United States (Sultan MA., 2023). “Exports, government debt and economic growth in sub‑ Saharan Africa”, this research focused on the impact of government debt on export-led growth in 44 sub-Saharan African countries from 2004 to 2023. It suggested that sub-Saharan African countries need to manage their debt levels to achieve export-led growth and recommended fiscal adjustments to reduce debt (Mensah, E., et al., 2024). “Sustainable development in African countries: evidence from the largest economies”, the study examines the impact of various factors on sustainability in 15 major African economies from 1999 to 2019. The findings highlighted the importance of: Education, Poverty, and ICT development reduction. It concluded that increasing trade liberalization volumes are linked to reduced sustainability. 

Furthermore, higher GDP per capita is associated with lower sustainability which is potentially due to unsustainable consumption patterns. So it recommended policies focusing on education, poverty reduction, and sustainable entrepreneurship to promote sustainable development in African countries (Angélica et al., 2024). “Revisiting the Gains from Trade in EMDEs: The Case of Selected East Asian and East African Economies”, the paper presented an exact price index to assess the welfare gains resulting from increased variety. According to the findings, African countries developed average welfare gains of 5.47% of GDP (0.20% per year) which is from 1995 to 2021, Asian countries (excluding Bhutan) gained 3.46% (0.13% annually). While on the other hand, some countries developed the highest welfare gains over the period including Bhutan, Mongolia, Rwanda, and Mozambique (Battogtvor, et al., 2025). “Sustainable development in Africa: A comprehensive analysis of GDP, CO₂ emissions, and socio‑economic factors”, this research examined the relationship between CO₂ emissions, economic growth, and socio-economic factors in 36 African countries from 1990 to 2020. It recommended integrated policies focusing on: renewable energy adoption, sustainable urbanization, and green growth strategies to achieve a balance between economic growth and environmental sustainability in Africa (Habimana Simbi, et al., 2025). “The contribution of tourism on GDP growth and sustainable tourism development in Africa”, this paper examined the contribution of tourism to GDP growth in 6 African countries (Egypt, Kenya, Morocco, South Africa, Tunisia, and Uganda) from 1999 to 2020. It provided insights into the complex relationship between tourism and GDP growth, highlighting implications for policymaking and economic development strategies in these African countries (Seraj, et al., 2025). “Real-time forecasting of German GDP based on a large factor model with monthly and quarterly data”, this paper presented a factor model for real-time short-term forecasting of GDP growth, utilizing a large set of monthly and quarterly time series. 

The model employed an EM algorithm with a principal components estimator to handle mixed frequencies and missing data. Using a novel German real-time dataset, the model's forecast accuracy is evaluated through a recursive experiment, assessing the impact of revisions, timely monthly observations, and comparing its performance to a quarterly-data-based factor model (Christian Schumacher, et al., 2008). “Forecasting and nowcasting real GDP: Comparing statistical models and subjective forecasts”, this study compared twelve statistical models and professional analysts' forecasting abilities for the euro area and its five largest countries (1996–2011). Summarizing information in a few factors and using all available monthly observations improves forecasting. The dynamic factor model excels, and analysts' judgmental forecasts contain valuable information that can enhance mechanical forecasts (W. Jos Jansen, et al., 2016; Sultan, 2023).

This paper provides a comparative statistical analysis of GDP growth patterns across selected African countries using time series models, addressing a gap in cross-country studies that often focus on a single economy. Furthermore, as we introduced the background information and reviewed related literature in this section, the second section will describe the data and methodology, the third section will present the empirical results and discussion, and the last section will conclude with key findings, limitations, and recommendations for future research.

This dataset provides comprehensive historical data on Gross Domestic Product (GDP) at a global level. The sample is about annual data that consists of Gross Domestic Product spanning from 1960 to 2023, categorized by African countries with the highest GDP in 2023: South Africa, Egypt, Kenya, and Ethiopia. This dataset is created from https://www.kaggle.com/datasets/stealthtechnologies/gdp-growth-of-african-countries. The data were analyzed with Econometrics Views (EViews).

ARIMA (Auto-Regressive Integrated Moving Average) is a statistical model used for forecasting and analyzing time series data. It is a combination of three components:

An Autoregressive (AR) Process: let Y_t represent the logged GDP at time t. Model Y_t  as: Where, c is a constant term representing the intercept,   are the coefficients and where u_t is an uncorrelated random error term with zero mean and constant variance σ^2. In which case Y_t is p th-order autoregressive, AR(p) process.

A Moving Average (MA) Process: It is simply a linear combination of white noise error termsWhere, (β_0,β_1,…,β_q) are the coefficients. 

Integration (I): accounts for non-stationarity in data by differencing.

So, the original time series is ARIMA (p,d,q) which is an autoregressive integrated moving average time series where p denotes the number of autoregressive terms, d  is the number of times the series has to be differenced before it becomes stationary and q  is the number of moving average terms (Gujarati, et al., 2009). Box-Jenkins (BJ) methodology is used to identify and estimate a statistical model which can be interpreted as the process that generated the sample data. In this study, we apply the following three steps of the (BJ) methodology:

Step 1: Identification & Estimation: which is, finding out the appropriate value of p, d and q

Step 2: Diagnostic checking: The researcher will select the optimal ARIMA (p, d, q) model based on the following criteria: larger significant coefficients, highest R-squared value, and Smallest values of: Akaike Information Criterion (AIC), Schwarz Criterion (SC), SIGMASQ (Box G.E.P., et al., 2015; Carter Hill R., et al., 2011).

Step 3: forecasting inside and outside the sample series

The ARIMA model was applied over 64 years, utilizing a stationarity test (Augmented Dickey-Fuller unit root test) on GDP series, as well as autocorrelation and partial autocorrelation function graphs to determine the appropriate differencing and transformation to achieve stationarity. The Auto-Regressive Integrated Moving Average (ARIMA) is primarily used for:

• Comprehensive analysis of African GDP. 
• Determining the optimal model for predicting GDP in African States. 
• Forecasting the African GDP growth over the next five years.

This section presents a comparative statistical analysis of GDP growth patterns across selected African countries using time series models and states the empirical findings of the time series analysis. First, we will describe the annual data series for the selected African countries. 

Then, we will examine the stationarity properties of each series using the Augmented Dickey-Fuller test to determine the appropriate order of differencing for the ARIMA models. After that, we will identify and estimate the optimal ARIMA (p, d, q) model for each country based on information criteria and diagnostic checks and then finally, we will evaluate the goodness-of-fit of the estimated models and present short-term forecasts of GDP to highlight future trends. The results of these analyses are presented in Table 1-13. The following table summarize the descriptive statistics of the highest GDP in Africa:

Table 1: Descriptive Statistics for Annual Data of the Highest Gross Domestic Product in Africa During 1960 – 2023.

The dataset in Table 1 demonstrates a statistical summary of Gross Domestic Product (GDP) figures for these African countries: South Africa, Egypt, Kenya, and Ethiopia.

South Africa records the highest GDP average at approximately $169.56 billion. Egypt ranks second in GDP average ($105.04 billion) but also shows considerable variability. On the other hand, Kenya and Ethiopia report significantly lower GDP averages ($24.50 billion and $23.81 billion, respectively), reflecting smaller economies. Although their standard deviations are lower in absolute terms, they are relatively high compared to their means, suggesting notable year-to-year variation. Overall, the data captures the disparities in economic scale and stability across these four African countries. The following figure describes the original series of the African sample:

As shown above Fig. 1, the original series has an exponential shape in all sample space of African countries. In addition, the Augmented Dickey-Fuller Test results are not statistically significant at 1%, 5%, 10% level, as shown in the table below:

Fig. 1: Annual Data on the Highest Gross Domestic Product in African Sample Series During, 1960 – 2023.

Table 2: Augmented Dickey-Fuller Test for Unit Root in Level.

We will eliminate the nonstationary by using the logarithm of the series, as shown in the table below: 

Table 3: Augmented Dickey-Fuller Test on Logarithms.

The Augmented Dickey-Fuller statistics of LGDP showed that the results are not statistically significant at 1%, 5%, 10% levels for all African sample series, hence, we conclude that the LGDP series have a unit root and is still non-stationary. The following table shows the result for Unit Root test after using 1st Difference of the logarithm:

 

Table 4: Augmented Dickey-Fuller Test for Unit Root in 1st Difference.

Table 4, shows that all the series are stationary after 1st Difference of the LGDP at 1%, 5%, 10% levels of significant.

The following table show the Correlogram of 1st difference of the LGDP for South Africa, Egypt, Kenya and Ethiopia:

Table 5: Correlogram of 1st Difference of the LGDP for the African Sample Series.

The Correlograms in Table 5 shows the auto-correlation (AC) and partial autocorrelation (PAC) functions for the first-differenced log (GDP) series, DLGDP. The Q-statistics in Correlogram of South Africa are significant in some AC and PAC, rejecting the null hypothesis of no autocorrelation up to each lag. 

The autocorrelation DLGDP function shows mixed positive and negative correlations, with significant spikes at lags 1,2,7. The PAC highlights notable values at lag 1,2 and 6. Hence, the final order 1, 2, 5 autoregressive moving average pre-estimation is performed on South Africa series. The following table show the estimated model of South Africa ARIMA:

Table 6: Estimated Model of ARIMA (p,d,q) of South Africa.

In the above table, the optimal model was selected according to number of significant parameters, R-squared, Akai Info. Criterion, Schwarz Criterion, Durbin-Watson stat and SIGMASQ. Model ARIMA (1,1,1), ARIMA (2,1,2) and ARIMA (5,1,2) were excluded to the low value of R-squared and low number of significant model parameters. We estimated the ARIMA models with q=7 and p=6, but they are excluded due to the lowest R-squared as well as no significant parameters. By comparing the rest of the model, we conclude that ARIMA (5,1,1) is the best model that satisfy highest R-squared value and the lowest values of the Akai Info. Criterion, Schwarz Criterion and SIGMASQ with significant values in all parameters. In Table 6, Q-statistics in Correlogram of Egypt, the AC values show significant spikes at lags 1,8 and 14 with Q-stat probabilities less than 0.05 from 18 up to 28, suggesting potential autoregressive behaviour at those lags. The PAC values help in identifying the direct effect of specific lags and hence pointing to notable influences at lags 1, 8, and 14. Therefore, the final order 1, 8, 14 autoregressive moving average pre-estimation is performed on Egypt series. The following table show the estimated model of Egypt ARIMA:

Table 7: Estimated Model of ARIMA (p,d,q) of Egypt.

Table 7 shows that an optimal model is ARIMA (14,1,8) due to the highest R-squared value and the lowest values of the Akai Info. Criterion, Schwarz Criterion and SIGMASQ with significant value parameters. In Table 5, Q-statistics in Correlogram of Kenya, the AC values show significant spikes at lags q=1, q=13 and q=14, suggesting potential autoregressive behaviour at those lags. The PAC values help in identifying the direct effect of specific lags which points to notable influences at lags p=1 and p=13. Therefore, the final order 1, 13, 14 autoregressive moving average pre-estimation is performed on Kenya series. The following table show the estimated model of Kenya ARIMA:

Model ARIMA (1,1,1), ARIMA (13,1,13), ARIMA (14,1,14) and ARIMA (14,1,14) were excluded to the low value of R-squared and a low number of significant model parameters.  By comparing the rest of the models, we conclude that ARIMA (14,1,13) is the best model that satisfy the highest R-squared value and the lowest values of Akai Info. Criterion, Schwarz Criterion and SIGMASQ with two significant value parameters.

 

Table 8: Estimated Model of ARIMA (p,d,q) of Kenya.

The Correlogram of DLGDP in Ethiopia in Table 5 show that the Q-statistic of AC and PAC are all significant, which rejects the null hypothesis of no autocorrelation up to each lag. Autocorrelation show significant values at lags q=1, q=4 and q=8, suggesting potential autoregressive behaviour at those lags. The PAC show significant values at lags p=1, p=4 and p=8. Therefore, the final order 1, 4, 8 autoregressive moving average pre-estimation is performed on Ethiopia series. The following table show the estimated model of Ethiopia ARIMA:

Table 9: Estimated Model of ARIMA (p,d,q) of Ethiopia.