Augmented Dickey-Fuller Test Research Articles

Predicting NEPSE Index: An ARIMA-Based Model

Purpose: This research aims to employ the Auto Regressive Integrated Moving Average (ARIMA) approach to forecast the Nepal Stock Exchange (NEPSE) index.Methods: Daily univariate time series data were taken from the NEPSE website and other sources for 27 years for a total 6143 daily time series data starting in 1997. The presence of unit roots was identified through an Augmented Dickey-Fuller (ADF) test, which ensures stationarity in data. Thereafter, estimation and evaluation of AR (autoregressive), MA (moving average), and ARIMA models were carried out.Results: The study reveals that the ARIMA (2,1,1) model is well fitted in predicting the NEPSE index, indicating its ability to capture temporal dependence and trends that exist within the data.Conclusion: It concludes the temporal dynamics of series highlighting both the short-term impacts of past shocks and longer-term adjustment towards equilibrium. The research work supports the efficacy of model in capturing and predicting the behaviour of NEPSE index, thereby adding in informed decision making and future projections based on proposed statistical foundations.

Management as a Factor of Socio-Economic Development of Small and Medium-Sized Businesses of Ukraine in Conditions of Instability

Small and medium-sized enterprises (SMEs) in Ukraine are increasingly challenged by ongoing economic instability, characterized by currency volatility, inflationary pressures, and uncertain political dynamics. This paper explores the role of management in the socio-economic development of small and medium-sized businesses (SMEs) under conditions of instability. Time series from 2001 to 2023 is analyzed for Ukraine. ADF and PP unit root test shows that data is stationery at first difference. ARDL bound test shows that time series data is cointegrated. Long-run estimates of ARDL technique show that management practices, socioeconomic development, research & development, technology adoption and employee skill & training have significantly positive relationship with SMEs growth rate, whereas, economic instability decrease the SMEs growth rate in Ukraine during studied time. Government of Ukraine should reform and bring new policies in all sectors especially manufacturing and production sector. Digitalization of the economy is foremost requirement of the Ukraine.

Vertical price transmission in agricultural markets in Ghana

The purpose of this study was to investigate the extent of price transmission along the agri-food supply chain in selected regions in Ghana. The extent of transmission was used to assess the efficiency and effectiveness of the agricultural marketing systems in the area. Efficient marketing systems are expected to reduce the issue of regional price fluctuations, encourage fair income distribution throughout the supply chain, and improve food security. The preliminary time series stationarity/unit root and seasonality tests were performed using the Augmented Dickey-Fuller test (ADF)/Kwiatkowski, Phillips, Schmidt, and Shin (KPSS) and Canova-Hansen seasonal stability tests respectively. Following the detection of statistically significant threshold effects by the Supremum Likelihood Ratio (Sup-LR) tests, the extent of price transmission was investigated using two-region threshold vector error correction models. The initial tests found that the monthly wholesale, retail, and producer price series for maize, cowpea, and yam used in the study were first difference stationary rather than seasonally integrated. The findings revealed that price signals in the agri-food markets were not fully transmitted across the supply chain. Thus, the extent of price transmission was generally low, creating unexploited arbitrage opportunities along the chain. The study identified high transfer costs (proxied by the threshold parameter) and actor-specific market power (as revealed by the Granger causality test) as the primary obstacles to effective market functioning in the area. Minimizing transfer costs through infrastructural development such as improvements in road networks linking farming communities and markets, access to price information, and regular stakeholder engagements could help improve the functioning of the agri-food markets.

Analysing Market Integration and Causality of Oilseed Crops: Key Insights and Challenges in Major Tamil Nadu Markets and Interstate Regions of India

Oilseed crops like Sesame and Groundnut experience significant price fluctuations due to factors like seasonal production patterns, their perishable nature, and risk involved in production and marketing of output. The farmers are further complicated by a lack of information about market conditions, including the timing of arrivals and prices. Market integration, which helps stabilize prices and improve the efficiency of the marketing system. This study focuses on analysing the market integration of major oilseed crops— Sesame, and Groundnut in India from January 2013 to January 2024. Johansen's cointegration test and Granger Causality test were applied to examine how prices in different markets are influence one another. The stationarity of the prices tested using the Augmented Dickey-Fuller test. The results confirmed that the prices are cointegrated, showing a strong interdependence between them. The analysis also revealed causal relationships between regions, such as bidirectional causality in the case of Sesame and Groundnut. The findings underscore the importance of further research to address production challenges, improve technical methods, and develop informed policies to manage the issues faced by oilseed crop growing farmers. This will help overcome obstacles in production and ensure a more efficient marketing system.

Embracing Technological Advancement: Assessing the Impact of Innovation on Sectorial Employment in Tanzania

Technological innovation is one of the most rapidly advancing and dynamic sector today. It drives growth across all sectors of the economy. However, this rapid growth presents both opportunities and challenges. Taking innovation into account, this study aims to assess the impact of technological innovation on three sectors which are agriculture, industrial, and service sectors. The study employed the autoregressive distributed lag model (ARDL), with data from 2000 to 2022 obtained from the World Bank (WB) and the World Intellectual Property Organization (WIPO). Three ARDL models were used to estimate employment in the agriculture sector, employment in the industrial sector and employment in the service sector with inflation (CPI) and interest rate (INT) as the control variables. The ADF (Augmented Dickey-Fuller) test, PP(Philip-Perron) test, Serial Correlation LM test, BG Heteroscedasticity, and Jarque Bera Normality test were utilized to ensure robust estimates of the models. The findings revealed that innovation has a significant positive influence on employment in the agriculture sector and service sector whereas the industrial sector is negatively influenced by innovation. Nevertheless, inflation has a significant positive effect on employment in the agriculture and service sectors but negatively affects employment in the industrial sector, where a lag in interest rate influence negatively employment in the agricultural sector. Relying on these findings, the study recommends an increase in expenditure on research and development, formulation of policies that will mainstream innovation in all sectors of the economy, and investing more in education and skills development

Financial factors influencing Profitability of Banque Pour Le Commerce Exterieur Lao Public (BCEL)

The research aimed to investigate the financial factors that influencing profitability of Banque Pour Le Commerce Exterieur Lao Public (BCEL). The objectives of this study are 1) to examine the financial factors that influencing profitability of BCEL in long-term period, and 2) to examine the financial factors that influencing profitability of BCEL in short-term period. The research target group is BCEL, and the instrument used to collect data is the financial statement of the BCEL in the period of 2011-2020 (40 quarter), including capital structure, working capital, firm size, revenue growth rate and non-debt tax shield, which is to find out the financial factors that determine BCEL's profitability. The data of the research model was tested quantitatively by using Engle and Granger method and Error Correction model, which tested its stationary by unit root in Augmented Dickey-Fuller (ADF) test and multi-collinearity by used EViews 9 Program. The results found that the data of each financial factor is stationary in First Difference, except that revenue growth rate is stationary in level order at 99% significant. And firm size variables had been multi-collinearity, thus eliminating the revenue growth rate and the firm size variables from the model. Therefore, 1) the financial factors that influencing profitability of BCEL in long-term period was influenced by three factors the working capital, which has positive relationship with profitability of BCEL; the non-debt tax shield which has positive relationship with profitability of BCEL, capital structure which has negative relationship profitability of BCEL, 2)the financial factors that influencing profitability of BCEL in short-term period was influenced by three factors such as: the change of working capital which has positive relationship with the change of profitability of BCEL, the change of the non-debt tax shield which has positive relationship with the change of profitability of BCEL, the change of capital structure which has negative relationship with the change profitability of BCEL, and the short-term equilibrium deviates to the long-term equilibrium with a velocity of 88.64%.

DIGITAL PAYMENTS AND FRAUD CONNECTION: INSIGHTS FROM THE INDIAN ECONOMY

In the dynamic world of digital transactions in India, the symbiotic relationship between convenience and vulnerability has become increasingly apparent. This study aims to know how digital payment and fraud connect in Indian economy. The primary objective of this study is to know the relationship between financial fraud with digital payment infrastructures, value of digital payments, and volume of digital payment. The data is collected through RBI’s official quarterly reports from September 2022 to May 2023. The collected time series data for all the variables has been analyzed for descriptive statistics. These series were tested for stationarity using Augmented Dickey–Fuller test (ADF - unit root test), Correlogram, and time series chart. The correlation and regression analysis has been performed on this time series data using SPSS and EViews software. From the correlation results this study reveals that there is no significant correlation between value and volume of fraud with payment infrastructure, value of digital payment, and volume of digital payment. The value of UPI transactions has a significant negative impact on digital payment fraud, indicating a potential protective effect.

Modeling and Forecasting High Frequency Currency Exchange Rates. A Comparative Study of ARIMA, ANN, and Hybrid ARIMA-ANN Models

Aims/ Objectives: The study develops comparative results on the modeling and prediction performance of the autoregressive integrated moving average (ARIMA), artificial neural network (ANN) and the hybrid ARIMA-ANN time series models for high frequency data. Methodology: The study made use of ARIMA, ANN, and hybrid ARIMA-ANN models to forecasts the East Africa Community countries' daily currency exchange rates data which were obtained from the Central Bank of Kenya website and covered the period from January 2017 to December 2023. Stationarity of the time series data was established using the ADF test. The Ljung Box test and ACF plots were used to establish and compare the goodness-of-fit of the resultant models while the Mean Absolute Percentage Error (MAPE) and Root Mean Squared Error(RMSE) values were used to compare the prediction performance. Results: The study established that the hybrid ARIMA-ANN methodolgy provided better-fitting models for the currency exchange rates data compared to ARIMA and ANN modeling strategies since all the Lyung Box test statistics had p values greater than 5%. Comparatively, the hybrid methodology registered lower MAPE and RMSE values hence had better prediction accuracy compared to ARIMA and ANN methods. Conclusion: The Hybid methodology improves the modeling and forecasting accuracy over the ARIMA and ANN models for high frequency time series data due to its ability to captures both the linear and nonlinear patterns in the time series data.

Assessing effects of agriculture and industry on CO2 emissions in Bangladesh

Climate change is a critical global issue, driven primarily by the continuous rise in carbon dioxide (CO2) levels. Addressing this challenge requires innovative solutions and proactive measures to mitigate its impact. This study investigates the impact of Bangladesh’s industrialization, agriculture, and imports on CO2 emissions, exploring both linear and asymmetric relationships to inform sustainable development strategies. Advanced modeling techniques, namely autoregressive distributed lag (ARDL) and nonlinear autoregressive distributed lag (NARDL) models are used to evaluate the impact of Bangladesh’s agricultural and industrial sectors on CO2 emissions. Time-series data ranging from 1990 to 2022 are analyzed to ensure data stationarity, employing the augmented Dickey-Fuller (ADF) test. Subsequently, the existence of non-linear associations is validated using the Brock-Dechert-Scheinkman (BDS) test, with further confirmation through bounds testing to establish both symmetric and asymmetric long-run cointegrating relationships. Long and short-run coefficients are assessed using linear and asymmetry ARDL models, revealing that industrialization contributes to increased carbon emissions in Bangladesh. While the ARDL model reports that the effect of agriculturalization on CO2 emissions is insignificant in the long-run, the asymmetry ARDL model suggests a rapid reduction in carbon emissions due to agriculturalization, observed both in the long and short-run. Additionally, imports have considerable impact on carbon emissions. Diagnostic tests have confirmed the adequacy of the model, while stability tests have validated the estimated parameters’ stability. Finally, the direction of association between variables is determined by applying linear and nonlinear Granger causality tests. This study underscores the importance of promoting sustainable industrial practices, enhancing agricultural efficiency, and regulating imports as pivotal strategies for mitigating CO2 emissions and achieving enduring environmental sustainability in Bangladesh.

The influence of climate change on crop production: Evidence from Somalia

The study examines the effect of climate change on crop production in Somalia for the period 1990 to 2022 obtained from the World Bank and FAOSTAT. Initial assessments were conducted on the data using various techniques, including the Correlation Matrix, Augmented Dickey-Fuller test, and Phillips-Perron unit root test. The findings from both the Bounds test and Johansen test demonstrate the existence of cointegration within the model. To estimate the parameter values of the regression model, three methods were employed: the Autoregressive Distributed Lagged (ARDL) model, Dynamic Ordinary Least Squares (DOLS), and Fully Modified Least Squares (FMOLS). The study's results demonstrate a positive and significant influence of foreign direct investment (FDI) on crop production. Specifically, the impact of FDI is found to be more pronounced in the long term compared to the short term. Similarly, the study finds that the harvested area and labor force have substantial positive impacts on crop production, both in the short run and long run. Based on the ARDL model results, the study finds that rainfall and temperature do not have a beneficial influence on crop production in both the short run and long run. This is becuase, Somalia is considered as one of the most susceptible countries to the effects of climate change globally. The paper advises Somalia's government to focus on developing heat-resistant crops to counter the opposing effects of temperature on crop production and ensure food security. It also requires a comprehensive agriculture funding-framework including emergency assistance.

Bio-inspired MXene membranes for enhanced separation and anti-fouling in oil-in-water emulsions: SHAP explainability ML

Optimizing membrane performance for efficient water treatment is crucial for sustainable development and environmental protection, aligning with UN SDGs. This study involves experimental design, statistical reliability of small data, and explainable machine learning (ML) using SHAP (Shapley Additive Explanations). The research uses ML models and statistical tests to ensure data reliability and stationarity and investigate various membranes’ fouling and separation efficiency (MX-CM, PDMX-CM, and SPDMX-CM). Stationarity tests, including the Augmented Dickey–Fuller (ADF) and Phillips–Perron (PP) tests, revealed that MX-CM is stationary at level (I(0)), while PDMX-CM and SPDMX-CM required first differencing (I(1)) to achieve stationarity. SHAP analysis showed that in the fouling study, higher values of PDMX-CM and MX-CM positively influenced model predictions, with SHAP values of +0.09 for Cycle, −0.06 for PDMX-CM, and −0.06 for MX-CM. In the separation efficiency study, Cycle had a neutral impact (0.00), PDMX-CM had a slight positive effect, and MX-CM had a slight negative impact. These findings highlight the importance of ensuring data stationarity and utilizing SHAP for model explainability in predicting membrane performance. Accurate preprocessing and model interpretation enhance decision-making and optimization in membrane fouling and separation efficiency studies, ensuring robust and reliable ML models.

A Time Series Study of Financial Sector Development and Original Sin in Nigeria

This study examined financial sector development and original sin in Nigeria financial market. Time series data was sourced from Central Bank of Nigeria Statistical Bulletin from 1990-2023. Original sin measured by Nigeria external debt per exchange rate, Capital market development as market capitalization to gross domestic product, Foreign exchange market as variation in naira exchange rate per US Dollar, banking sector development as percentage total bank assets to gross domestic product, money market development as insurance total assets to gross domestic product, Money market development as value of money market instrument to gross domestic product. The study employed descriptive statistics and multiple regression models to estimate the relationship that exists between the dependent and independent variables. The null Hypotheses (H0) were tested at 0.05 level of significance, Ordinary Least Square (OLS), Augmented Dickey Fuller Test, Johansen Co-integration test, normalized co-integrating equations and parsimonious vector error correction model were used to conduct the investigations and analysis. The study found that 57.0% variation on original sin can be traced and explained by variation on the independent variables as formulated in the regression model. However, the F-Statistics and the F-probability justifies that the model is significant and adequate in explaining variation on the dependent variable. The β coefficient shows that capital market development have negative effect on original sin, foreign exchange market have positive effect on original sin, banking sector development have negative effect on original sin, insurance sector development and money market development have positive effect on original sin. From the findings, the study concludes that the independent variables determine positively and negatively original sin in Nigeria. We recommend that the need for policies to deepen the capital market as this can cushion the effect of the negative effect of external borrowing and domiciled in Nigeria currency rather than international currency. There should be institutionalized policies to enhance the value of the naira against other international currencies as this can reduce the pressure of exchange rate variation in international debt and international monetary environment. Public expenditure should be directed to the productive sector of the economy as this can enhance the productive capacity of the economy and reduce the negative effect on balance of payment and other macroeconomic variables. Policies should be advanced to reduce external borrowings; this can reduce the debt burden and reduce the incidence of original sin in the financial market.

Forecasting of Electricity Consumption by Seasonal Autoregressive Integrated Moving Average Model in Assam, India

Sustainable electricity consumption, which is about balancing economic growth, social development and environmental protection are the core principles of the Sustainable Development Goal (SDG). Accurate forecasting of electricity consumption is very important for attaining SDG - 7 which aims to ensure access to affordable, reliable, sustainable and modern energy for all. Through this paper, attempt is made to forecast monthly electricity consumption in Assam. For this purpose, one of the most widely used time series techniques, viz., Seasonal Autoregressive Integrated Moving Average (SARIMA) is applied by considering the time period April, 2013 to February, 2023 to study the seasonal influence on the electricity consumption in Assam. By applying Augmented Dickey Fuller test, it is observed that the data series becomes stationary at first order difference and the result of Canova Hansen test reveals that no seasonal differencing is required for our considering time period. SARIMA (1,1,1) (1,0,1)12 has been selected for forecasting purpose by following the results of Akaike Information Criterion. By analyzing the model statistics, residual ACF and PACF plots of the selected model, it is found that SARIMA (1,1,1) (1,0,1)12 can be effectively recommended for forecasting of monthly electricity consumption in Assam with Mean Absolute Percentage Error as 3.12%.

Box Jenkins ARMA Model for Forecasting Bangladesh's Remittance Inflow

This study uses Eviews software in order to determine the best Box-Jenkins ARMA model for forecasting the growth rate of remittances in Bangladesh by utilizing time series data from the year 1980 to 2022. In our study, we used the Augmented Dickey-Fuller Test (ADF Test) to check the stationarity of the time series data. This test shows that data is stationary at level 0, i.e., Remittance (0). By performing several selection criteria for the lowest SIGMASQ and the lowest value of AIC and BIC, we obtain ARMA (1, 1), which is the best model for forecasting remittances in Bangladesh. Diagnostic tests additionally demonstrate the stability and acceptability of the parsimonious model that has been given for remittance prediction in Bangladesh. The study's findings reportedly demonstrate that Bangladesh's remittance inflows are declining. The article makes the case that, in order to increase remittance inflows into Bangladesh, the country's emigration policy needs to be strengthened.

Capital Flight and Nigeria Economic Growth

The study explored the impact of capital outflow in Nigeria and focused on its implications for the country's emerging economy. It reviews relevant literature and theories. It applied the Augmented Dickey-Fuller test to analyze the time series data obtained for the investigation. The ARDL bounds tests for cointegration was used to determine the relationships among the variables. The autoregressive distributed lag method was also employed to evaluate the short- and long-term associations between the explanatory factors and economic growth. Findings reveal a limited correlation between capital outflow and economic growth, whereas foreign direct investment showed a minor negative impact in the long run. It was also revealed in the investigation that leadership style and Governance contribute to capital flight in the country. Recommendations were to the effect that, creation of a favourable economic environment was necessary to reduce capital outflow, promote trade liberalization, and encourage regional integration to enhance market access.

EFFECTS OF FINANCIAL INCLUSION ON POVERTY REDUCTION, SAVINGS AND NIGERIA ECONOMIC GROWTH: 1980 -2022

This study examined the financial inclusion and Nigerian economic growth for the period 1980-2022. The study considered the following three objectives; to examine the significant impact of financial inclusion on the Nigerian economic growth, evaluate the impact of financial inclusion on poverty reduction in Nigeria and to ascertain the impact of financial inclusion no savings growth in Nigerian economy. Secondary time series data were used to carry out the empirical analysis. The study employed the aid of vector error correction model (VECM) approach, Augmented Dickey-Fuller (ADF) and Phillips-Perron tests, Co-integration Test and ECM. Based on the above econometric and statistic techniques conducted, it was observed that financial inclusion has significant positive impact on the Nigerian economic growth. Our results indicated that financial inclusion has significant positive impacts on poverty reduction in Nigeria. Furthermore, the result reported that financial inclusion has significant positive impact on the Nigerian savings growth within the study period (1980-2022). These empirical results do support that; One percent decrease in the interest rate (ITR), inflation rate (IFR) and exchange rate (EXR) at lag (-2) will lead to [31% (ITR)-2), 53%(IFR)-2), and 8%(EXR)-2)] increases on the aggregate saving (ASE) Nigeria economy. One percent increase in the financial inclusion proxy by; deposit from the rural areas (DRA), loan to rural areas (LRA), account owners of any type (AA) and electronic money banking/payment system (EMB) at lag (-2) will lead to [38%(DRA)-2), 29%(LRA)-2), 59%(AA)-2) and 03%(EMB)-2)] increases on Per capita income (PCI) respectively in Nigeria. Based on these findings, the researcher recommends that; Nigeria governments should fund financial inclusion programs preferring financial literacy as a national strategy for financial inclusion because it is relatively cheaper to educate the population about financial management and the benefits of using formal financial services. Stable electricity supply to drive the infrastructural facilities provided by banks, telecommunication companies and other related service providers such availability and affordability of financial services in Nigerian monetary authority (CBN) should increase the number of formal account ownership by building up trust securities in financial institutions operation in Nigeria, remove all obstacles for account ownership such as income and age bracket bias, distance in location and education discrimination in the delivery and use of financial services

A comprehensive statistical analysis of Malaria dynamics in the Adamawa region of Cameroon, from 2018 to 2022

Malaria remains a prominent public health concern in Cameroon, with the potential for epidemic outbreaks, necessitating a robust understanding of its dynamics. This paper uses routinely collected surveillance data from health facilities in the Adamawa Region since January 2018. By applying statistical analysis, this study aims to enhance comprehension, enable data predictions, and facilitate informed decision-making for public health policy implementation. Focusing on weekly health districts data spanning from 2018 to 2022, our analysis employs key statistical metrics for central tendency, data spread, distribution shape, and variable dependence. The study reveals distinctive trends, highlighting peak malaria transmission periods consistently occurring between August and November each year. The highest weekly recorded case count in any health district reached 1,294. The data exhibits leptokurtic distributions, skewed to the left of the median. And in 2022, 11% of the population was reported to have contracted malaria. Despite an overall region-wide average growth rate of -1.21% over the past five years, maintaining vigilant attention to this critical health issue is imperative. Auto dependence analysis indicates that observations are weekly correlated, assuming the time series as stationary. The stationarity has been confirmed by ADF and KPSS tests that we performed. This comprehensive data analysis helps our understanding of the malaria landscape in the Adamawa Region of Cameroon. The paper also recommends the inclusion of additional variables in data collection for a more holistic perspective. These findings provide a basis for the formulation and implementation of targeted interventions by relevant stakeholders, aiding in the prediction of future cases and ultimately contributing to the effective management of malaria in the region.

ARIMA-Based forecasting of monthly rainfall in Mandi district, Himachal Pradesh

ABSTRACT To anticipate monthly rainfall time series, autoregressive integrated moving average (ARIMA) modelling was performed using R studio. For a period of 30 years (in mm), the monthly rainfall data were gathered for eight localities in the Mandi district of Himachal Pradesh: Bharol, Chachiyot, Jogindernagar, Karsog, Kataula, Mandi, Sarkaghat, and Sundernagar. The augmented Dickey–Fuller test was performed to determine whether the rainfall data were steady before applying the ARIMA model. The minimal values of the Akaike information criterion, Bayesian information criterion, autocorrelation function, and partial autocorrelation function were used to select the best models. The best fit was determined to be ARIMA (0,0,2) (2,1,0)12 for five stations and ARIMA (0,0,0) (1,1,0)12 for the remaining three stations. A box test is performed to validate the ARIMA model and verify the autocorrelation in the data. Using the ARIMA model, forecasts are made for the 10 years (2021–2030). The validity and performance of the ARIMA models were evaluated using error statistics (mean absolute error = 34.65, root-mean-square error = 33.58, and R2 = 0.93). The projected data's mean and standard deviation were close to the actual data. As a result, the ARIMA model's monthly rainfall prediction parameters were satisfactory.

Modelling Petrol Prices in Kenya from 2014 to 2023 Using Sarimax Model: A Case Study of Nairobi County

The requirement for petrol price information is crucial for majority of enterprises. This is because fluctuations in petrol prices impact inflation hence affecting daily lives of citizens. In analyzing the prices of petrol, researchers have employed several models but encountered various limitations. These limitations include; the Error Correction Model can examine only one co-integrating association. The Vector Autoregression (VAR) model does not account for the structural changes in the data. Additionally, the AutoRegressive Integrated Moving Average (ARIMA) model does not take into consideration the seasonal component in the data. The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model assumes that over time the volatility is constant. Moreover, the Seasonal Autoregressive Integrated Moving Average (SARIMA) model does not integrate the external factors. Hence in this study Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) model was employed since it captures seasonality in data and incorporates the exogenous variables. The research’s aim was to model prices of petrol in Kenya for the period between 2014 to 2023 with exchange rates as an external factor. Secondary data was obtained from Energy and Petroleum Regulatory Authority (EPRA), Kenya National Bureau of Statistics (KNBS) and Central Bank of Kenya (CBK) websites. R software was used to analyze the data. By the use of historical data of petrol prices and exchange rates, the study sought to fit the best Seasonal Autoregressive Integrated Moving Average with Exogenous Variables (SARIMAX) model, validate the model and predict the petrol prices. The petrol price data was found to be non-stationary using Augmented Dickey Fuller test (ADF). Regular differencing was conducted to make the data stationary. Seasonal differencing due to seasonality component available in the data was also performed. Best SARIMAX model was chosen from various SARIMAX models according to Box-Jenkins methodology which uses least Akaike Information Criterion (AIC) value. SARIMAX (0,1,1)(2,1,2)<sub>12</sub> model was selected since it had least Akaike Information Criterion (AIC) value of 656.3733 and the model validated using the hold out technique. The forecasts errors from the training set were; Mean Squared Error (MSE)=10.4970, Root Mean Square Error (RMSE)=3.239911, Mean Absolute Percentage Error (MAPE)=2.309268% while those from the testing set were; Mean Squared Error (MSE)=3271.1012, Root Mean Square Error (RMSE)=57.193542, Mean Absolute Percentage Error (MAPE)=26.695390%. There was less error in the training set than in the testing set as it was expected hence the model suited the data well and could be used for future predictions. The model was then used for five year forecast into the future. This study’s findings will offer sound suggestions to policymakers, businesses and consumers. This study recommends a model to be fitted using other factors affecting petrol prices and fitting Fourier terms, Behavioral Assessment Tools (BATS) and Trigonometric Box-Cox ARMA Trend Seasonal (TBATS) models.

Economic Growth, Industrialization, and CO2 Emissions in Pakistan: Insights from ARDL Modeling

This study explores how industrialization, economic growth (measured by GDP per capita), and CO? emissions have interacted in Pakistan over nearly five decades, from 1974 to 2022. It also considers the influence of population growth and foreign direct investment (FDI) on this relationship. To analyze the data, the ARDL model was used, ensuring the reliability of the results by confirming stationarity with the Augmented Dickey-Fuller (ADF) test. The results showed that in the long run, a 1% increase in GDP per capita and FDI inflows results in respective increases in CO? emissions of 0.33% and 0.061%. Still, a 1% rise in industrial activity lowers CO? emissions by 0.34%. In the short run, a 1% rise in GDP per capita and FDI reduces CO? emissions by 0.21% and 0.020%, respectively. Conversely, a 1% increase in industrial activity causes emissions of 0.29%. These findings are in line with the Environmental Kuznets Curve (EKC) theory, which holds that CO? emissions initially rises when a nation industrializes but as the technology advances and more rigorous rules are followed, the level of CO? emissions decreases. Based on these results, policies emphasizing investments in renewable energy, strict environmental rules enforced, and support of clean technologies and sustainable industrial practices are suggested.