
==== Front
Heliyon
Heliyon
Heliyon
2405-8440
Elsevier

S2405-8440(24)12305-5
10.1016/j.heliyon.2024.e36274
e36274
Research Article
Forecasting and unveiling the impeded factors of total export of Bangladesh using nonlinear autoregressive distributed lag and machine learning algorithms
Akhter Tanzin a
Ratna Tamanna Siddiqua a
Ahmed Ferdous ferdous.ahmed@iubat.edu
b⁎
Babu Md. Ashraful c
Hossain Syed Far Abid d
a Department of Quantitative Sciences, International University of Business Agriculture and Technology, (IUBAT), 4 Embankment Drive Road, Sector -10, Uttara, Dhaka, Bangladesh
b Department of Environmental Science, International University of Business Agriculture and Technology, 4 Embankment Drive Road, Sector -10, Uttara, Dhaka, Bangladesh
c Department of Physical Sciences, Independent University, Bangladesh, Dhaka, 1229, Bangladesh
d BRAC Business School, BRAC University, Dhaka, 1212, Bangladesh
⁎ Corresponding author. ferdous.ahmed@iubat.edu
15 8 2024
15 9 2024
15 8 2024
10 17 e362743 12 2023
27 7 2024
13 8 2024
© 2024 The Authors
2024
https://creativecommons.org/licenses/by-nc-nd/4.0/ This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Rising global oil prices are a major challenge for an emerging oil-importing nation such as Bangladesh. The majority of prior research on the economic effects of an oil price shock has concentrated on developed countries, with emerging economies receiving comparatively less attention. Bangladesh is vulnerable to price shocks due to its rising oil consumption over the past decade. This study aims to investigate how changes in oil prices would affect Bangladesh's total export earnings and to forecast the overall export volume. This study utilized a nonlinear autoregressive distributed lag (NARDL) approach to account for the asymmetric behavior of oil prices from 1991 to 2021. To assess the accuracy of predictions, the study employed the Prophet forecasting model and the Long Short-Term Memory (LSTM) method. Additionally, the symmetry test revealed a nonlinear relationship between export volume and oil price but a linear relationship between inflation and export volume. According to the NARDL assessment, both positive and negative oil shocks increase export earnings over the long run. The short run summary clarifies that both positive and negative changes in oil prices exert a significant negative effect on exports. Also, Inflation influences export earnings negatively in the short run but positively over the long term. Moreover, using machine learning methods, it was found that the LSTM method outperforms the prophet model in prediction performance with a low root mean square error (RMSE) of 1.88. Also, the analysis revealed policymakers that the export sector requires diversification to reduce its exposure to oil price shocks.

Keywords

Oil price shock
Export volume
Machine learning
NARDL
LSTM
==== Body
pmc1 Introduction

Energy has emerged as a fundamental resource in any growing economy and has been noted to be a significant disseminator of volatility shocks to other sectors of the economy [1,2]. It is the backbone of modern industrial production, consumption, and distribution. The economic and social progress of Bangladesh relies on energy. It requires a substantial amount of energy for overall development. Crude oil is the most important nonrenewable power source in Bangladesh. Besides that, the cornerstone of mass commodities is fuel [3]. Crude oil has recently emerged as one of the most tradable commodities. Several economists believe oil price volatility affects worldwide trade and economic development [4]. The economies of both oil exporters and importers are affected by shifts in gasoline costs [4].

Since 1970, the oil industry has experienced significant fluctuations [5], including the global financial crisis of 2008 [1]. But the emergence of the COVID-19 pandemic led to an unprecedented decline in oil prices. Because of this pandemic, oil consumption has been drastically cut, particularly in transportation. The precipitous fluctuations in global fuel affordability have an enormous impact on the country's economic resilience [6,7]. Many scholars, like Charfeddine and Barkat [8] and Taghizadeh-Hesary et al. [9], demonstrate that a sharp increase in the international crude price is advantageous for oil exporting countries while posing a challenge for oil-importing nations. A hike in oil prices increases the revenue of oil producing countries while increasing the production costs of oil-importing countries. In contrast, for oil-producing countries, a plunge in oil prices will reduce the government budget, whereas for oil-consuming countries, a drop in oil prices will shrink production costs.

The energy, transportation, and industrial sectors of Bangladesh are reliant on the importation of crude oil. As per the 2021 annual report of the Bangladesh Hydrocarbon Unit, the country's crude oil imports in the fiscal year 2020–2021 amounted to 1,307,261.92 metric tons, with Saudi Arabia and the UAE being the primary sources of such imports [10]. Moreover, the export sector is crucial to the economic development of Bangladesh, as increased export earnings can stimulate economic growth [5]. An uncertainty in export revenues could adversely affect economic expansion because export duties are a significant source of revenue for financing public expenditures. The main export industries of Bangladesh are textiles, shipbuilding, fish and seafood, jute, and leather products. Since the mid-1980s, the country's exports have been steadily shifting from jute and jute products to RMG, reflecting the transition from an agriculture-driven economy to a manufacturing-based one.

However, the Export Promotion Bureau (EPB) reported a decline in export earnings from USD 39.33 billion to USD 33.60 billion in 2020 due to the COVID-19 pandemic, which also reduced worldwide exports by 8.98 percent [11]. In a recent literature review, Goodell [12] expressed concern regarding the economic implications of COVID-19 and noted the potential long-term impact of the pandemic on financial services. Further, during the period of high global uncertainty, Bangladesh has demonstrated a history of growth and development. Furthermore, strong export volumes, stable macroeconomic prospects, and a steady inflow of remittances have all contributed to Bangladesh's sustained and robust economic growth over the past two decades. Moreover, by 2026, Bangladesh will no longer be classified as a Least Developed Country (LDC) by the United Nations and will enter the developing economy category. Besides, for emerging nations like Bangladesh, increasing fuel prices will boost inflationary pressure and the cost of living. Fuel price increases will also boost the production expenses of all businesses and industries that rely on energy ([13], Jesus et al., 2020). Subsequently, several scholars have analyzed the impact of the oil price shock on both global and local economies and concluded that fluctuations in oil prices are interconnected with significant global events and have the potential to trigger economic growth or downturns [14]. Moreover, the price volatility of an economy rises with inflation. It reduces project profitability. Thus, conscientious investment methods reduce investment, which slows economic growth. Furthermore, a lower export volume and a higher inflation rate have the combined effect of reducing the country's international competitiveness. Additionally, a stable and low inflation rate encourages higher investment, which boosts export revenue. Consequently, stable inflation makes this sector more price-competitive globally.

From the preceding discussion, it is easy to posit that the oil price and the inflation rate have a huge influence on yearly total export earnings in Bangladesh. Hence, it is crucial to forecast the export patterns for the upcoming years in order to mitigate the susceptibilities to oil price fluctuations and uphold a steady inflation rate for the socioeconomic well-being of the nation. It has been noted that numerous researchers have utilized machine learning and deep learning approaches for the purpose of accurately predicting multivariate time series data [15,16]. For example, Lin et al. [17] introduced a deep-learning-based graph-focused multivariate time series prediction model for coagulant dosage determination in water treatment. In addition, the model predicts coagulant dosage better than time series forecasting. In comparison to conventional approaches, Duan et al.[18] discovered that machine learning provided a considerable improvement. They employed machine learning techniques to forecast monetary policy moves and associated macroeconomic uncertainties. Additionally, Chu et al. [19] have reported that machine learning algorithms demonstrate a high degree of accuracy in predicting stock returns. Mathonsi and van Zyl [20] used mortality modeling and a hybrid statistical-deep learning method to forecast multivariate time series. The Multivariate Exponential Smoothing Long Short-Term Memory (MES-LSTM) algorithm predicts time series, and the Cox proportional hazards model analyzes mortality in the suggested method. They found that the recommended strategy outperformed the benchmark techniques in prediction accuracy.

Numerous academic investigations have been conducted to examine the association between oil price fluctuations and various macroeconomic indicators, including economic growth ([21]; Driouche et al., 2020; [8]), inflation ([[22], [23], [24], [25]]), unemployment rate [[26], [27], [28]], exchange rate [[29], [30], [31], [32]], and stock market (Cañete et al., (2022); [33]). Additionally, a number of academic investigations have examined the correlation between export revenue and macroeconomic indicators, including economic growth [34] and exchange rate [35,36]. A significant number of earlier studies focused on investigating how changes in oil prices affect other macroeconomic factors instead of to export earnings. Prior studies have mainly focused on industrialized nations, with little interest given to developing oil-importing countries, such as Bangladesh. To the best of the author's information, this is an inaugural study in Bangladesh to investigate how oil price shocks affect overall export earnings and forecast export behavior for the next few years. Hence, utilizing annual time series data from 1991 to 2021, this study assesses the effect of inflation and the oil price shock on total export volume in Bangladesh and also forecasts the total export volume for the next five years, from 2022 to 2026. Based on earlier research revealing nonlinear behavior of oil price shocks and macroeconomic variables, this work has incorporated the recently developed nonlinear autoregressive distributed lags (NARDL) model by Shine et al. [37]. A symmetry test was conducted to corroborate the results of the NARDL bounds test. The analysis showed a linear pattern between inflation and export earnings but no linear association between oil prices and export earnings. Furthermore, a machine learning model called Prophet and a deep learning model named Long Short-Term Memory (LSTM) have been employed to perform the forecasting of total export volume in Bangladesh.

Hence, the framework of this paper continues: Section 2 examines the empirical literature. Section 3 describes the data, model technique, and variables. The fourth section discusses the empirical testing, while the fifth section summarizes the study.

2 Literature review

2.1 Theoritical review

Bangladesh derives the majority of its national revenue from the export sector. Export-oriented factors significantly contribute to Bangladesh's economic expansion. Additionally, Bangladesh's export growth is substantially driven by ready-made garments (RMG), which comprise approximately 84 percent of the country's merchandise exports. The main raw materials used in the export industry are imported from foreign markets, as are the raw materials used in other export sectors, such as the industrial and agricultural sectors. The export sector can be significantly impacted by fluctuations in global oil prices. Studies have suggested some theoretical mechanisms through which fluctuations in oil prices can impact the overall export earnings of an economy. The "wealth shift effect" is a transmission path via which oil price shocks lead to the transfer of income from energy consumers to oil exporters. One explanation for this is that a spike in oil prices will drive up production costs, which in turn will drive down consumer demand in a nation that imports oil [38]. Conversely, increases in oil prices will furnish financial assets conducive to heightened production, thereby bolstering the GDP growth of nations that export oil.

Another channel is supply-demand mechanisms. Within the supply-side channel, an increase in the price of oil will result in a cost effect [39], as it serves as the fundamental input for industrial production. Additionally, it will increase production expenses, which will lower productivity and investment. The supply transmit also turns into a straight path for the oil price shock. Through the demand-side pathway, rising oil prices will raise the price level, reduce real income for consumers, and result in lower output and consumption. Additionally, it raises the interest rate [40]. The final reason is the interest rate channel. Oil price increases have an indirect impact on the macroeconomic condition through the interest rate channel because policymakers will raise interest rates in response to projected inflation brought on by higher oil prices and demand for money [41].

Furthermore, various causes, such as recessions, geopolitical risk, and the dynamic relationship between supply and demand, can account for the asymmetric nature of oil price variations. The theory is based on the mid-1980s oil price collapse, which led to a 50 percent reduction in the global oil price and disrupted the linear relationship between oil prices and economic development. Subsequently, throughout the 2008 financial crisis, the COVID-19 pandemic, and the geopolitical dispute between Russia and Ukraine, there was a notable manifestation of volatile and swiftly fluctuating oil prices. Subsequently, throughout the 2008 financial crisis, the COVID-19 pandemic, and the geopolitical dispute between Russia and Ukraine, there was a notable manifestation of volatile and swiftly fluctuating oil prices. This geopolitical conflict and economic crisis significantly impacted the energy sector. As a result, transportation and production expenses escalate, which has a detrimental impact on the export sector.

The relationship between inflation and exports is also based on fundamental assumptions. For instance, the hypothesis known as "the Phillips curve" suggests that higher inflation can stimulate economic growth by reducing the unemployment rate [42], which is also influenced by a rise in export volume. Further, the demand-pull inflation theory states that aggregate demand—the overall demand for goods and services—exceeds total supply. Excessive demand causes prices to rise for a diverse array of goods and services, ultimately resulting in an inflationary surge. In addition, a boost in net exports and increased expenditure by consumers, businesses, or the government may contribute to a rise in aggregate demand.

2.2 Empirical literature

Growing export earnings can influence the overall economy of a country, and oil price fluctuations have a vital impact on the country's export revenue as they influence both production and utility costs [13]. Bangladesh, as a net oil importer country, suffers greatly from fuel price hikes. Several academics have explored how changes in oil prices affect various macroeconomic factors in recent decades. For example, Alfalih [26] examined the association between the oil price (OP) and the unemployment rate (UER) in Saudi Arabia, utilizing the linear ARDL approach. The author discovered an adverse association between the oil price and the UER. Karlsson et al. (2018) and Tien (2022) reported similar results for Norway and Vietnam. In contrast, Cuestas and Gil-Alana [43] discovered conflicting results regarding Central and Eastern Europe, Kisswani and Kisswani [44] for the United States, Nusair [28] for Canada and the United States, and Kocaarslan et al. (2020) for the United States when the NARDL methodology was applied. They discovered that higher unemployment rates are correlated with increases in oil prices.

Using a vector autoregressive (VAR) methodology, Salisu et al. [45] assessed the oil price movement on real GDP in 33 nations, both developed and developing. The researchers found that industrialized countries had a more pronounced adverse effect on real GDP compared to emerging economics. Multiple research studies have also investigated the relationship between oil price trends and economic growth using the NARDL technique, as suggested by Driouche et al. (2020), Charfeddine and Barkat [8], and Kisswani [21]. The economic performance of Malaysia, Qatar, and Asien countries was found to improve with an increase in oil prices by Shangle and Solaymani [46], Charfeddine and Barkat [8], and Kisswani [21].

Several studies have examined whether oil price volatility has a detrimental effect on environmental sustainability adopting the NARDL model [[47], [48], [49], [50], [51]]. Okwanya et al. [47] observed that rising oil prices mitigate carbon emissions in African oil-importing and exporting nations. Sama et al. [48] discovered a negative relationship between Cameroonian oil prices and CO2 emissions. Subhan et al. [49] and Sreenu [50] noticed that oil consumption in India is a trigger for CO2 emissions. Ali et al. [51] found that increases in oil prices reduce carbon emissions and improve the quality of the environment in South Africa. Aliyev et al. [22] discovered that oil prices had a decisive influence on inflation in Azerbaijan by employing the linear ARDL model. In contrast, an asymmetric relationship between oil prices and inflation was observed by Zakaria et al. [23] and Lacheheb and Sirag [4] for South Asian nations and Algeria. Kumar et al. [52] established an asymmetric relationship between oil prices and stock prices. By employing a NARDL model, the researchers discovered a significant relationship between fluctuations in crude oil prices and stock prices. Okere et al. [33] analyzed Nigeria's stock market-oil price asymmetry from January 1995 to December 2019. It was noted that a positive shock to the price of oil benefits Nigeria's stock market. The asymmetric relationship between oil price volatility and exchange rates for established and developing nations has been the subject of numerous studies employing the NARDL model, including [30,[53], [54], [55]]. Moreover, many academics have studied oil price movements and economic uncertainty [56,57].

Furthermore, there have been limited studies that have investigated the relationship between the amount of exports and macroeconomic variables, particularly by considering export volume as a dependent variable. For example, Urgessa [35] investigated the relationship between the fluctuation of exchange rates and export earnings in Ethiopia. The author demonstrated that exchange rate volatility has an asymmetric impact on overall export revenue using the NARDL model. Positive fluctuations reduce overall export earnings, while negative movements have no significant impact. Sugiharti et al. [36] reported comparable results. They noted that the ARDL and NARDL models both imply that changes in exchange rates have a detrimental impact on Indonesian exports. In contrast, Raeeni et al. [5] investigated the associations between energy consumption and export in Iran from 1967 to 2015. They discovered that there was no correlation between energy consumption and exports.

The behavior of econometric variables holds significant importance for the overall economic growth of a nation. That is why, recently, researchers have assembled machine learning and deep learning methods with the conventional econometric model to study the behavior of the variables as well as forecast their patterns [2,58]. Utilizing natural gas and crude oil prices, Bouteska et al. [2] suggested an artificial neural network approach and a non-linear oriented time-delayed neural network procedure to forecast energy prices. Charfeddine et al. [59] employed basic econometric time series modeling, as well as machine learning and deep learning techniques such as XGBoost, LSTM, SVR, and the Prophet model, to predict electricity usage in Qatar. They observed that econometric time series models predicted electricity usage better than machine learning models. Yang et al. [60] proposed deep learning models for predicting global trade using export and import data. Specifically, they presented three models: a multilayer perceptron (MLP), a convolution neural network (CNN), and a hybrid model that combines MLP and CNN. The findings showed that, in terms of accuracy and robustness, the hybrid model performed better. A hybrid model created by Efat et al. [58] that combines a deep neural network model with an adaptive trend estimated series (ATES) model fared better at sales forecasting than any of the methods already in use. Chaturvedi et al. [15] utilized the SARIMA, LSTM RNN, and Fb Prophet models to predict the energy demand in India. For the period spanning 2019 to 2024, the authors choose to employ Fb Prophet to generate future energy forecasts. Safi et al. [61] investigated whether oil prices could predict exchange rates using deep learning methods, and results supported that the 10.13039/100014976 LSTM model outperformed other traditional models in predicting exchange rates and that oil prices were significant predictors of exchange rates in several countries. Shen et al. [62] proposed an efficient method for forecasting global trade by employing the LSTM network. According to the results, the developed network model exhibited superior forecasting accuracy compared to conventional time series forecasting techniques such as ARIMA and exponential smoothing. Dave et al. [63] proposed a hybrid model combining autoregressive integrated moving average (ARIMA) and long short-term memory (LSTM) for predicting Indonesian exports. The study showed that the recommended hybrid model excels over conventional ARIMA and LSTM models in terms of predicting accuracy.

Recently, in the context of Bangladesh, several significant works have been undertaken by different academics regarding the consequences of oil price volatility and inflation on economic growth and other macroeconomic variables. As an example, the effects of vital macroeconomic variables on Bangladesh's budget deficit were analyzed by Alam et al. [64] during the years 1980–2018. They used the VECM approach, which exhibited inflation, economic growth, and the money supply negatively affecting the budget deficit. Amin et al. [65] investigated the relationship between the oil price and the real exchange rate of USD for the economy of Bangladesh. The ARDL model was utilized to suggest that a boost in oil prices would ultimately result in an increase in the currency rate. However, the currency rate is unaffected by fuel prices in the short run.

According to the above literature analysis, academics are more interested in scrutinizing the consequences of fluctuations in oil prices on macroeconomic indicators than export earnings, particularly for developed nations. Researchers have also conducted numerous studies on developing nations, yet Bangladesh has garnered minimal attention. Researchers also focus less on forecasting a country's export behavior. Our study's goal is to fill this gap, examine the nexus between oil price fluctuations and export volume, and predict export volume patterns. However, the following key investigations are addressed in this research:1. Is there a long-term equilibrium relationship between the defined variables?

2. Does the relationship between the variables exhibit asymmetry or symmetry?

3. What is the effect of a sudden increase in oil prices on export revenue in the short and long run?

4. What are the short- and long-term impacts of a decrease in oil prices on export revenue?

5. What impact does inflation have on export earnings?

6. Forecasting of export earnings along with oil prices and inflation rates for the next couple of years.

7. Assess the performance of Bangladesh's export earnings forecast model.

3 Data and methodology

3.1 Description of data

The present empirical study employed annual data spanning from 1991 to 2021. The following variables are utilized for this research: crude oil price (OP), which is measured in dollars per barrel; consumer price index (CPI), which serves as a proxy for inflation and is measured as an annual percentage change; and total export earnings (EX), which is measured in billions of dollars. As independent variables, inflation and crude oil prices were used, with total export income as a dependent variable. The data on total export earnings and inflation were extracted from world development indicators, while the oil price data were collected from the British Petroleum (BP) Statistical Review of World Energy 2022. Further, all variables were transformed to natural logarithms, which minimize skewness and express elasticity. Table 1 provides further details about the data, variables and their sources.Table 1 Description of the variables.

Table 1Variables	Abbr.	Description	Time Span	
Export earnings	lnEX	Total export earnings represent the overall export volume of Bangladesh in a year and are expressed in billions of dollars.
Source: https://databank.worldbank.org/source/world-development-indicators	1991–2021	
Crude oil price	lnOP	The yearly price of crude oil is determined by averaging the prices of Brent, WTI, and Dubai crude oil and is expressed in dollars per barrel.
Source: https://www.bp.com/content/dam/bp/business-sites/en/global/corporate/pdfs/energy-economics/statistical-review/bp-stats-review-2022-full-report.pdf	1991–2021	
Inflation	lnCPI	The consumer price index (CPI) is taken as a proxy for inflation and measures the percentage change in the price of a standard basket of goods and services over time.
Source: https://databank.worldbank.org/source/world-development-indicators	1991–2021	

3.2 Model specification

3.2.1 Non-linear autoregressive distributed lag (NARDL) model

The fundamental goal of this article is to determine how oil prices and inflation affect Bangladesh's export income. As a result, we performed the following empirical analysis using the Phillips curve method:(1) lnEXt=π0+π1lnOPt+π2lnCPIt+μt

Where lnEX is log of export earnings, lnOP is log of oil price, lnCPI is log of consumer price index, π specifies the vector of long run coefficients. Other researchers have used enhanced Phillips curve methodologies, notably Sek [14], Olanipekun et al. [24], and Lacheheb and Sirag [4]. However, the asymmetric behavior of export revenues, oil price changes, and CPI inflation cannot be captured by the linear formulation of Eq. (1). Thus, our research expanded on the nonlinear ARDL model derived by Shin et al. [37], which segments the regressor into two categories: negative and positive partial sum components. The NARDL framework has been utilized to study asymmetric interactions in further studies recently. The NARDL model is a single equation model that permits simultaneous investigation of non-stationarity and nonlinearity in an unrestricted error correction framework and provides better results with small samples [66]. Further, the NARDL approach is applicable whether the study variables are integrated at order 1 or 0, or a combination of both, whereas the classical Johansen co-integration approach requires the same order of integration of all underlying variables [67]. In accordance with Shin et al. [37], we assess the subsequent nonlinear asymmetric cointegrating model:(2) lnEXt=θ0+θ1lnOPt++θ2lnOPt−+θ3lnCPIt++θ4lnCPIt−+ϵt

where θi denotes the long run coefficients vector, and the effects of oil price and consumer price index fluctuations are captured by lnOPt+, lnOPt−, lnCPIt+ and lnCPIt−, that can be partitioned into a positive and negative partial sum in Eqs. (3), (4), (5), (6):(3) lnOPt+=∑i=1tΔlnOPt+=∑i=1tmax(ΔlnOPi,0)

(4) lnOPt−=∑i=1tΔlnOPt−=∑i=1tmin(ΔlnOPi,0)

(5) lnCPIt+=∑i=1tΔlnCPIt+=∑i=1tmax(ΔlnCPIi,0)

(6) lnCPIt−=∑i=1tΔlnCPIt−=∑i=1tmin(ΔlnCPIi,0)

The following is an explanation of Eq. (2) in terms of an asymmetric error-correction model Shin et al. (2014):(7) ΔlnEXt=α0+ρlnEXt−1+β1+lnOPt−1++β1−lnOPt−1−+β2+lnCPIt−1++β2−lnCPIt−1−+∑i=1p−1ωiΔlnEXt−i+∑i=0qμ1,i+ΔlnOPt−i++∑i=0qμ1,i−ΔlnOPt−i−+∑i=0qμ2,i+ΔlnCPIt−i++∑i=0qμ2,i−ΔlnCPIt−i−+ϵt

where θ1+=−β1+ρ,θ1−=−β1−ρ and θ2+=−β2+ρ,θ2−=−β2−ρ indicates the long-term positive and negative coefficients. Additionally, the short-term adjustment of the oil price and consumer price index is obtained by μi,1+,μi,1−,μi,2+,μi,2−.

This empirical study proceeds as follows: First, a unit root test was employed to ascertain the degree of integration of the variables. Despite being appropriate for I(0) and I(1) variables, the autoregressive distributed lag model fails to account for I(2) series. Thus, unit root testing is necessary to prevent the I(2) combination. To accomplish this, the Augmented Dickey Fuller (ADF) and Phillips-Perron (PP) tests were utilized. The second step includes evaluating Eq. (7), which can be obtained using ordinary OLS, and the Akaike Information Criterion (AIC), which is chosen as the optimal lag length. Third, we incorporate the bounds test method adopted by Pesaran et al. [67] and Shin et al. [37], and the modified F-test to explore the long-run dependence among the variables. The F-statistic examines the combined null hypothesis of no cointegration H0:ρ=β+=β−=0 to the alternative of cointegration H0:ρ≠β+≠β−≠0. There are two crucial bounds used in the related testing procedure: the upper bound and the lower bound. The null hypothesis is deemed valid if the resultant F-statistic value is smaller than the lower critical bound; otherwise, the test is inconclusive if it falls within the critical boundaries. The symmetry test is utilized in step four, and the null hypothesis of long-run symmetry is H0:β+=β−, and any one of the following approaches can be used to depict short-run symmetry: H0:∑i=0qμ+=∑i=0qμ−.The final step is to implement the NARDL approach to obtain the cumulative dynamic multiplier influence of a 1 % increase or decrease in lnOPt−1+,lnOPt−1−,lnCPIt−1+, and lnCPIt−1− respectively, on lnEXt in an asymmetric way, as below in Eqs. (8), (9):(8) mp+=∑j=0p∂lnEXt+j∂lnOPt+,mp−=∑j=0p∂lnEXt+j∂lnOPt−,p=0,1,2,…..

(9) mo+=∑j=0o∂lnEXt+j∂lnCPIt+,mo−=∑j=0o∂lnEXt+j∂lnCPIt−,o=0,1,2,…..

Note that as p→∞, then mp+→θ1+ and mp−→θ1−, and as o→∞, then mo+→θ2+ and mo−→θ2−.

The following Fig. 1 summarizes the methodology of this study.Fig. 1 Visualization of the Methodology (Formulated by author).

Fig. 1

3.2.2 Prophet model

The Prophet forecasting model (Taylor and Letham, 2017) is a time series forecasting algorithm developed by Facebook's Core Data Science team. It is designed to handle a wide range of time series patterns, including trend changes, seasonality, and holiday effects, and to provide interpretable forecasts and uncertainty estimates.

Let yt be the time series value at time t, and let gt, st, and ht be the trend, seasonality, and holiday components, respectively. The Prophet model can be written as in Eq. (10):(10) yt=gt+st+ht+εt

Where εt is the error term at time t.The trend component is modeled using a piecewise linear or logistic function, which allows for changes in the growth rate over time. Specifically, let tc be the time of the trend change, and let Δt be the rate of change in the trend before and after the change point. Then the trend component can be written as follows in Eqs. (11), (12):(11) gt=k(t)+Δt(t−tc)

for t≥tc(12) gt=k(t)

for t<tc

Where k(t) is a piecewise linear or logistic function that is fit to the data.

3.2.3 Long short-term memory (LSTM) model

The Long Short-Term Memory (LSTM) [68] model is a recurrent neural network that is well-suited for sequence modeling and prediction. It is particularly useful when working with long sequences of data, where traditional neural networks may struggle to capture long-term dependencies.The LSTM architecture is based on a set of memory cells that allow the network to selectively retain or discard information over time. These memory cells are controlled by a set of gates that regulate the flow of information into and out of the cell. Specifically, there are three types of gates: the input gate, the forget gate, and the output gate.

Let xt be the input vector at time t, h{t−1} be the hidden state at time t−1, and c{t−1} be the memory cell at time t−1. The input gate it, forget gate ft, and output gate ot are defined as follows, respectively, in Eqs. (13), (14), (15):(13) it=σ(Wixt+Uih{t−1}+bi)

(14) ft=σ(Wfxt+Ufh{t−1}+bf)

(15) ot=σ(Woxt+Uoh{t−1}+bo)

where Wi,Wf,Wo,Ui,Uf,Uo,bi,bf, and bo are the learnable parameters of the model, and σ is the sigmoid function.The memory cell at time t is updated as follows in Eq. (16):(16) ct=ft⊙c{t−1}+it⊙tanh(Wcxt+Uch{t−1}+bc)

where⊙ denotes element-wise multiplication, and Wc, Uc, and bc are the learnable parameters of the model.The hidden state at time t is computed in Eq. (17) as follows:(17) ht=ot⊙tanh(ct)

A supervised learning approach is utilized to train the LSTM model, in which the input sequence and associated target sequence are supplied as input. The objective is to optimize the network in such a way that the margin of error between the expected outcome sequence and the actual target sequence is minimized. Mean-squared error (MSE) or cross-entropy loss are common examples of loss functions that are employed for this purpose.

4 4. results and discussion

4.1 Results from NARDL frame work

4.1.1 Econometric validation and parameter estimation

The precondition for time series analysis is that the variables being studied should exhibit stationarity; hence, the ADF and PP unit root tests were utilized. An overview of the findings is shown in Table 2. For optimal lag order, Schwarz's information criteria (SIC) was applied, adding intercept and time trend to level but simply intercept to the first difference. The stationarity of the variables under consideration can be derived from their respective levels. Notably, lnCPI is stationary at level, which implies that the variable is categorized as I(0). Conversely, lnEX and lnOP display non-stationarity at level but attain stationarity at the first difference, thus indicating an I(1) nature for these variables. Despite the absence of second-order integration (I(2)) among the variables, we can use the ARDL framework to access a cointegration relationship for both linear and nonlinear models.Table 2 Unit root Test Assesment.

Table 2Variables	Level	First Difference	
ADF	PP	ADF	PP	
lnEX	−2.54	−2.631	−7.897***	−7.983***	
lnOP	−1.449	−1.511	−4.664***	−4.594***	
lnCPI	−4.038**	−4.074**	−7.257***	−10.407***	

The cointegration test is employed using the unrestricted error correction methodology of the F-test on the joint hypothesis that no cointegration exists between selected variables. Assessments of the model estimation process for symmetric and asymmetric co-integration are shown in Table 3. The evalutions of the bounds test confirm no co-integration for the linear formulation, as the resultant F-statistic value of 2.38 falls below the lower critical bound of 3.53 at a significance level of 5 %. However, for non-linear specification, the F-statistic value of 7.78 surpasses the upper critical point of 4.306 at the 5 % significance level, indicating the presence of co-integration among study variables.Table 3 Overview of the co-integration bounds test.

Table 3Model layout	F-statistic	95 % lower bound	95 % upper bound	Decision	
Symmetric ARDL	2.38	3.53	4.43	No co-integration	
Asymmetric ARDL	4.79	3.272	4.306	Co-integration	
Note: Critical values are observed by of Pesaran et al. [67].

Before estimating the non-linear ARDL approach, we additionally examine the long-run, short-run, and joint symmetry of our assigned predictor variables. The outcomes are displayed in Table 4. The results disclose that the null hypothesis fails for the long-run, short-run, and joint symmetry for lnOP at a 5 % level of significance. We cannot reject the null hypothesis for lnCPI.Therefore, we proceed with our analysis by exploring the following NARDL model in Eq. (18):(18) ΔlnEXt=α0+ρlnEXt−1+β1+lnOPt−1++β1−lnOPt−1−+β2lnCPIt−1+∑i=1p−1ωiΔlnEXt−i+∑i=0qμ1,i+ΔlnOPt−i++∑i=0qμ1,i−ΔlnOPt−i−+∑i=0qμ2,iΔlnCPIt−i+ϵt

Table 4 Results of coefficient symmetry test.

Table 4Variable	F-statistic	Conclusion	H0: Coefficient is symmetric
H1: Coefficient is asymmetric	
Long-run	Short-run	Joint (long-run & short-run)	
lnOP	0.04**	0.02**	0.04**	Reject Ho		
lnCPI	0.07	0.19	0.16	Accept H0	
Note: **, refers significant at 5 % levels.

After verifying the presence of a cointegration link, the NARDL model can be estimated, and the resulting long-term statistical values are presented in Part A of Table 5. It has been noticed that, in the context of crude oil prices, significance is verified for both positive (lnOP+) and negative (lnOP−) long-run indicators. The computed long-run coefficients of lnOP+ and lnOP− are 0.33 and −0.38, respectively. Accordingly, a 1 % rise in oil prices results in an increase in aggregate export earnings of 0.33 %. Similarly, a reduction of 1 % in oil prices increases total export earnings by 0.38 %. Consequently, our findings imply that the negative adjustments have a larger impact. The long-run estimation results contradict the conclusions reached by Khan et al. [69], who found no evidence of a long-term asymmetry relationship between Bangladesh's economic development and oil prices. Moreover, the findings show that CPI has a positive and statistically notable long-run effect on export earnings. The coefficient can be interpreted as, a 1 % increase in CPI inflation leads to a 1.06 % growth in export revenue. It can be concluded that a devaluation of the domestic currency can potentially encourage foreign buyers to buy more products, which will stimulate export earnings.Table 5 Non-linear ARDL estimation result.

Table 5Dependent variable: ΔlnEXt	
Variables	Coefficients	t-statistic	Standard Error	p-value	
Part A: Long-run specification	
lnOP+	0.33	3.80	0.3178	0.0010	
lnOP−	−0.38	−3.41	0.0882	0.0025	
lnCPI	1.06	3.34	0.1132	0.0029	
Part B: Short-run specification	
ΔlnEXt−1	−0.56	−3.37	0.1664	0.0082	
ΔlnCPI	−0.54	−5.31	0.1032	0.0005	
ΔlnOP+	−0.41	−3.97	0.1037	0.0032	
ΔlnOP−	−0.36	−4.21	0.1232	0.0026	
ECMt−1	−0.73	−6.56	0.1136	0.0001	
Part C: Diagnostic test results	
Test	P-value	Hypothesis	Summary	
Jarque-Bera	0.3492	H0: Residuals are normal	H0 is accepted	
Ramsey-RESET	0.4687	H0: Functional form is correctly specified	H0 is accepted	
LM	0.2773	H0: No serial correlation	H0 is accepted	
ARCH	0.4738	Ho: Homoskedasticity	H0 is accepted	
Note: **, refers significant at 5 % levels.

Global oil prices are subject to disruption due to various factors, such as geopolitical risk, supply and demand scenario, actions made by the Organization of Petroleum Exporting Countries (OPEC), catastrophic events, production expenses, and storage facilities. For every nation, but particularly for those whose economy depend on the import of crude oil, it is a strategic issue. Since Bangladesh is a net oil importer, the outcome of the long-run estimation has significant implications for the country's economy. The result reveals that any hike in oil prices will boost the country's total export income. As a result, it may argue that growing global oil prices will have no effect on the local market in Bangladesh due to the country's administrative fuel oil pricing policy. In addition, the government of Bangladesh offers subsidies for the import of natural gas and crude oil [70]. This supports the oil market's stability. In an effort to manage the oil market, the government has recently permitted the private sector to engage in the importation, refining, and market selling of fuel products [71]. Also, one can conclude that a surge in the worldwide price of oil will result in an upswing in international commodity prices, which will have a beneficial effect on export income [72]. Numerous researchers have reached similar conclusions regarding oil-importing nations by employing alternative macroeconomic indicators; for instance, Sarwar et al. [73] observed that a surge in oil prices leads to a corresponding escalation in inflation in Pakistan. The economic performance of Malaysia was found to improve with an increase in oil prices by Shangle and Solaymani [46]. Sreenu [50] and Shastri et al. [74] discovered that rising oil prices cause India's economic growth and CO2 emissions to increase. Furthermore, Kisswani [21], Okere et al. [33], Zakaria et al. [23], and Shangle and Solaymani [46] have also found similar results in their studies investigating the associations between positive shocks in oil prices and several macroeconomic variables. The study's results contradict the findings stated [75]. Therefore, the results of the study are consistent with previous research.

Besides, it has been noted that a decrease in oil prices leads to an increase in the total export volume of Bangladesh. Additionally, the results verify that a decrease in the oil price has a greater effect on export earnings. A decrease in oil prices will result in a reduction in the expenses associated with raw materials, input costs, and production costs, hence contributing to a rise in the overall export revenue of the country. Crude oil import demand has increased over the past decade due to the accelerated development of export-oriented sectors and the rapid growth of the service sector. Bangladesh also imports raw materials for the agricultural and other industrial sectors, as well as for the export and service industries, from foreign markets. Consequently, a decrease in fuel prices would be advantageous for Bangladesh. Similar findings were obtained by Malik et al. [75] and Shastri et al. [74] in their investigations on the effects of a negative shock on oil prices. This finding contradicts the research results of Nusair and Olson [76] and Okere et al. [33] in their respective studies.

The results of short-run dynamics are captured in Table 5, Part B. The empirical findings of nonlinear ARDL reveal that both positive (lnOP+) and negative (lnOP−) oil shocks have a significant negative influence on exports in the near term. The estimated short-run coefficient for a positive shock in oil prices is −0.41, which amplifies the fact that an increase of 1 % in oil prices leads to a slump in export revenue of 0.41 %. Therefore, it may conclude that the steepest increase in fuel costs will disrupt the short-term recovery of industries and businesses in Bangladesh. Similarly, the calculated coefficient for a negative oil price shock is −0.36, indicating that a 1 % fall in oil prices boosts export revenue by 0.36 %. Consequently, it can be suggested that a plunge in oil prices could accelerate the growth of export earnings by reducing production costs since Bangladesh is heavily reliant on imported crude oil. Moreover, in the shortrun, the consumer price index exhibits an adverse influence on total export earnings. The findings point out that a 1 % rise in inflation leads to a 0.54 % drop in overall export revenue.

Based on the aforementioned analysis, the research findings suggest that Bangladesh, an oil-importing nation, experiences advantageous effects from downward fluctuations in oil prices, both in the short run and over a long period of time. It boosts a country's economy by creating trade surpluses. Furthermore, it contributes to the alleviation of unemployment by creating employment prospects within the export industry.

However, to justify the reliability of the NARDL model, some diagnostic tests were conducted. This research employed the Jarque-Bera (J-B) test to investigate the normality of error, the Ramsey RESET test to investigate model specification, the Autocorrelation Conditional Heteroskedasticity (ARCH) test for heteroskedasticity, and the LM test for serial autocorrelation. The outcomes of all tests are exhibited in Part C of Table 5. The outcomes recommendthat the NARDL model successfully satisfies all the diagnostic tests.The CUSUM and CUSUM Square tests, as proposed by Brown et al. [77], were employed to verify the consistency of the coefficients. Fig. 2 depicts the graphs of these tests and confirm that the model's parameters are highly stable, as the test statistics lie under the 5 % significance line.Fig. 2 CUSUM and CUSUMSQ tests for parameter stability.

Fig. 2

4.1.2 Granger causality test

The Granger causality test determines if one time series can predict another [78]. Table 6 presents the outcome of Granger Causality.Table 6 Summary of Granger Causality test.

Table 6Null Hypothesis	F-Statistic	P-value	Decision	
LNINF does not Granger Cause LNEXPORT	5.02632	0.0150**	Rejected	
LNOIL does not Granger Cause LNEXPORT	3.73696	0.0386**	Rejected	
LNOIL does not Granger Cause LNINF	3.51487	0.0458**	Rejected	

The results of the causality check indicate the presence of an unidirectional causal association from the inflation rate to the overall export earnings and from the oil price fluctuations to total export volume. Moreover, an unidirectional causal connection exists between the volatility of oil prices and the rate of inflation.

4.2 Multivariate time series Forecasting based on prophet Model and long short-term memory (LSTM) model

It is observed that lnEX has strong co-integration with lnOP and lnCPI where lnOP has non-linear and lnCPI has linear correlations with lnEX (see Table 3, Table 4). In this section, LSTM and Prophet models are used to forecast the export earnings for the next five years from 2022 to 2026 in Bangladesh, along with oil prices and the inflation rate.

4.2.1 Forecasting with prophet model

The Prophet model concerns the variety of seasonality, like yearly, monthly, etc., and it can detect the growth of the data by itself. Here lnOP and lnCPI are used as additional regressors to forecast the lnEX values for the next five years. To obtain the future five-year values of lnOP and lnCPI, univariate forecasting has been performed by the same Prophet model, where the logistic growth function is used to forecast the lnOP. Fig. 3 shows the forecasted yearly export earnings in comparison to the observed real export earnings. Also, Fig. 4(a) and (b) show the forecasted yearly oil prices and forecasted yearly inflation rates for the next five years in Bangladesh. From Fig. 3, it is clearly observed that the lnEX fitted with the historical data and follows the same increasing trend as the previous years. Similarly, Fig. 4(a) shows the non-linearity of the forecasting of oil prices.Fig. 3 Forecasted yearly export earnings (in $billions) by prophet model.

Fig. 3

Fig. 4 (a). Forecasted Yearly Oil Prices USD per barrel by Prophet Model, (b). Forecasted Yearly Inflation Rates (%) by Prophet Model.

Fig. 4

Furthermore, the average cross-validation scores for the 216 days of the horizon in Table 7 and the mean absolute percentage error (MAPE) for the 365 days of the horizon from Fig. 5 demonstrate the validation of this prediction. Here the following Prophet model is used with yearly seasonality and interval_width = 0.95 for this forecasting:Table 7 Cross-Validation scores for forecasting with Prophet Model.

Table 7Evaluation indicators	MSE	RMSE	MAE	MAPE	MDAPE	SMAPE	
Values	36.45	4.72	4.28	0.23	0.16	0.22	

Fig. 5 Cross-Validation score for forecasting with Prophet Model.

Fig. 5

model = Prophet(yearly_seasonality = True, interval_width = 0.95)

model.add_regressor('oil_price')

model.add_regressor('inflation')

model.fit(data)

4.2.2 Forecasting with long short-term memory (LSTM) model

In this study, the fitted the LSTM Recurrent Neural Network model was applied to forecast future export earnings for the next five years. This experiment used two LSTM hidden layers with three and four neurons, respectively and one input layer with three neurons and one Dense layer as an output layer with three neurons for the output of lnEX, lnOP, and, lnCPI respectively. Also, the ‘tanh’ activation function for the two hidden LSTM layers was utilized in the following model:

model = Sequential(.)

model.add(LSTM(3,activation = 'tanh',return_sequences = True, input_shape=(train_X.shape[1], train_X.shape[2])))

model.add(LSTM(4, activation = 'tanh'))

model.add(Dense(3))

In this model, 80 % of the data was used for training and 20 % for cross-validation, and Fig. 6 shows that after 1800 epochs, the test root mean square error (RMSE) value reduced to 10.48.Fig. 6 Train-Test loss score for forecasting with LSTM Model.

Fig. 6

Fig. 7 demonstrated that the forecasted yearly export earnings data nicely fitted and forecast the future five years of export earnings, which are nearly 40 billion USD. From Fig. 8, Fig. 9, it is observed that the forecasted yearly oil prices and inflation rates data are fitted with the real data; also, graphs show the stability of oil prices and inflation rates for the next five forecasted years.Fig. 7 Forecasted yearly export earnings (in $billions) by LSTM model.

Fig. 7

Fig. 8 Forecasted Yearly Oil Prices (USD per barrel) by LSTM Model.

Fig. 8

Fig. 9 Forecasted yearly inflation rates (%) by LSTM model.

Fig. 9

4.2.3 Performance testing of prophet and LSTM models

In this section, the performance of the Prophet and the LSTM models were tested by using the full dataset to forecast yearly export earnings. The tests' validity was assessed using various metrics, including RMSE, MAPE, mean square error (MSE), and coefficient of determination (R2), which show accuracy at lower results. Table 8 shows the test scores for MAPE, MSE, RMSE, and R2 values for the Prophet and LSTM models. Based on the findings, it can be concluded that the LSTM model produces more accurate results than the Prophet model. With respect to MAPE, MSE, RMSE, and R2, the LSTM model possesses considerably lower values (0.06, 3.53, 1.88, and 0.98, respectively) in comparison to the Prophet model's values (0.45, 16.74, 4.09, and 0.92, respectively). Which implies that the LSTM model significantly minimizes the error compared to the error from the Prophet model. The results align with previous studies conducted by Dave et al. [63], Shen et al. [62], Solís et al. [79], Jia and Yang [80], and Safi et al. [61], demonstrating that the LSTM model is better than alternative machine learning and traditional time series forecasting methods.Table 8 Performance testing scores for Prophet & LSTM Models to forecast yearly export earnings by using the full dataset.

Table 8Evaluation indicator	Model	
Prophet	LSTM	
MAPE	0.45	0.06	
MSE	16.74	3.53	
RMSE	4.09	1.88	
R2	0.92	0.98	

5 Conclusions and policy implications

5.1 Conclusions

This study incorporates time series data covering 1991–2021 to assess the influence of fluctuations in oil prices and inflation on the aggregate export volume of Bangladesh and forecast the total export volume using the machine learning method. The research includes a NARDL bounds testing methodology utilizing both short- and long-run estimation techniques and the LSTM and Prophet models to predict the total export earnings of Bangladesh. This study also incorporates stationary tests (ADF and P–P) to check the order of integration of the variables.

The conintegration (bounds) test reveals the existence of a long-run relationship between Bangladesh's export earnings and selected macroeconomic indicators in this study. Before applying the NARDL method, a symmetry test was applied to confirm the asymmetric behavior between selected variables. The result of the symmetry test confirms the asymmetric connection between oil price and export volume, whereas a linear connection was found between inflation and export volume. The study applies several diagnostic tests, including the CUSUM and CUSUMSQ tests, to check the model's stability, and the NARDL model satisfies all the diagnostic tests.

The study result provides that in the long run, both positive and negative oil changes enhance export volume, and it rises more significantly in response to negative oil shocks than to positive shocks. Consequently, this finding provides significant evidence for the presence of a stable asymmetry. The short-run result reveals that a positive change in oil price decreases total export earnings and a negative change in oil price enhances total export earnings. The findings also demonstrate that the consumer price index stimulates export earnings significantly. Afterward, the Prophet and the LSTM models were used to forecast the export performance in Bangladesh. According to the findings, the LSTM approach is the most optimal approach for accurately predicting export volume, with a lower MAPE of 0.06 %.

5.2 Policy implications

The empirical findings of this study have implications for Bangladesh's policymakers, as it is an emerging nation that relies entirely on imported crude oil to meet its energy needs. The demand for crude oil increases every year due to population growth, urbanization, industrialization, and economic expansion. The export sector is the biggest source of foreign currency for Bangladesh. Unfortunately, this sector can be seriously hit by fluctuations in global oil prices. The study results indicate that a decline in the price of oil is more beneficial for the Bangladeshi economy, both in the long run and in the in the short run. Therefore, the government should strengthen macroeconomic regulations and energy security systems, particularly oil security and price controls, as every sector, from transportation to industry, is dependent on crude oil. In addition, they must undertake proactive and stringent fiscal policies that enhance the reduction of state expenditures and currency devaluation.

Though the increase in fuel prices has a ripple effect on both production and transportation expenses, the government should increase subsidies in the energy sector. But implementing an immediate augmentation of the subsidy amount poses a formidable challenge for a developing country such as Bangladesh. Moreover, in the long term, the expansion of energy export subsidies could potentially be facilitated through the implementation of reforms in taxation, infrastructure, and national asset planning.

While acknowledging the challenges associated with government intervention in the volatile oil market, it is recommended for policymakers to prioritize the development and utilization of sustainable energy alternatives. Because a substantial increase in oil prices will adversely influence the country's energy industry and export performance.

6 Research limitations

This study has certain drawbacks. 1) This research simply examines three macroeconomic indicators; future studies may use more macroeconomic variables to enhance explanatory capacity. 2) The export sector can be influenced by several factors; however, this research only focuses on two of them. Additional study can incorporate a broader range of explanatory variables, such as government and private sector investment in the export industry, imported raw materials, geopolitical risk, and other relevant aspects. 3) This study utilizes yearly data spanning from 1991 to 2021. Subsequent research can explore a more extensive sample size in order to obtain a more precise forecast. 4) This study employs only two machine learning techniques; future studies may employ a wider range of machine learning techniques.

CRediT authorship contribution statement

Tanzin Akhter: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Investigation, Formal analysis, Data curation, Conceptualization. Tamanna Siddiqua Ratna: Writing – review & editing, Writing – original draft, Visualization, Validation, Software, Resources, Methodology, Formal analysis, Data curation, Conceptualization. Ferdous Ahmed: Writing – review & editing, Writing – original draft, Supervision. Md. Ashraful Babu: Formal analysis, Data curation. Syed Far Abid Hossain: Writing – review & editing, Writing – original draft, Visualization, Supervision.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
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