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Chemical Engineering & Development

Journal of Science and Engineering

Vol. 08 / Nº 01

e – ISSN: 3028-8533

ISSN – L: 3028-8533

Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 75

ARIMA vs. Hybrid Models with Machine Learning for Forecasting

Ecuador's GDP

ARIMA vs. Modelos Híbridos con aprendizaje automático para pronóstico del PIB de Ecuador

Leonor Alejandrina Zapata Aspiazu

*; Edwin Haymacaña Moreno

; Francisco Javier Duque-Aldaz

; Félix Genaro Cabezas

García

; Raúl Alfredo Sánchez Ancajima

Received: 09/28/2025 – Accepted: 12/02/2025 – Published: 01/01/2025

Research Articles

Review

Articles

Essay Articles

* Corresponding

author.

This work is licensed under a Creative Commons Attribution-NonCommercial-Share Alike 4.0 (CC BY-NC-

SA 4.0) international license. Authors retain the rights to their articles and may share, copy, distribute, perform,

and publicly communicate the work, provided that the authorship is acknowledged, not used for commercial

purposes, and the same license is maintained in derivative works.

Abstract.

The analysis of Gross Domestic Product (GDP) is essential for understanding Ecuador's economic dynamics and guiding strategic decisions in contexts of high

macroeconomic volatility. The purpose of the study was to estimate and forecast Ecuador's short-term GDP growth rate using robust and validated statistical

models. Historical GDP series (1965–2023) obtained from the Central Bank of Ecuador were used. Stationarity tests (ADF, KPSS), correlograms, and information

criteria (AIC, BIC) were applied to select appropriate ARIMA models. The analysis was performed using EViews 12, generating projections for the period 2024–

2027 under optimistic, pessimistic and expected scenarios. The results showed that the Ecuadorian GDP series was not stationary at its original level, which

required the application of the first difference to stabilise the mean. The identified ARIMA model incorporated autoregressive and moving average components,

whose coefficients were statistically significant. The model residuals did not show autocorrelation, confirming its validity. The projections generated for the period

2024–2027 indicated moderate growth under optimistic, pessimistic and expected scenarios. These results were consistent with official estimates, validating the

Box-Jenkins methodology as an effective tool for national economic forecasting. The study provides useful empirical evidence for national economic planning,

validating the applicability of ARIMA models in GDP analysis. In addition, it promotes interdisciplinary approaches between economics and engineering,

strengthening the technical capacity to address macroeconomic problems in contexts of high structural uncertainty.

Keywords.

Economic growth, Gross Domestic Product, Ecuador, Arima and Box-Jenkins models, Economic forecasting, Macroeconomic planning.

Resumen.

El análisis del Producto Interno Bruto (PIB) resulta esencial para comprender la dinámica económica de Ecuador y orientar decisiones estratégicas en contextos

de alta volatilidad macroeconómica. El estudio tuvo como propósito estimar y pronosticar la tasa de crecimiento del PIB ecuatoriano a corto plazo mediante

modelos estadísticos robustos y validados. Se utilizaron series históricas del PIB (1965–2023) obtenidas del Banco Central del Ecuador. Se aplicaron pruebas de

estacionariedad (ADF, KPSS), correlogramas y criterios de información (AIC, BIC) para seleccionar modelos ARIMA adecuados. El análisis se realizó con EViews

12, generando proyecciones para el período 2024–2027 bajo escenarios optimista, pesimista y esperado.Los resultados evidenciaron que la serie del PIB ecuatoriano

no era estacionaria en su nivel original, lo que requirió la aplicación de la primera diferencia para estabilizar la media. El modelo ARIMA identificado incorporó

componentes autorregresivos y de media móvil, cuyos coeficientes fueron estadísticamente significativos. Los residuos del modelo no presentaron autocorrelación,

lo que confirmó su validez. Las proyecciones generadas para el período 2024–2027 indicaron un crecimiento moderado bajo escenarios optimista, pesimista y

esperado. Estos resultados fueron consistentes con estimaciones oficiales, validando la metodología Box-Jenkins como herramienta eficaz para el pronóstico

económico nacional. El estudio aporta evidencia empírica útil para la planificación económica nacional, validando la aplicabilidad de modelos ARIMA en el

análisis del PIB. Además, promueve enfoques interdisciplinarios entre economía e ingeniería, fortaleciendo la capacidad técnica para abordar problemas

macroeconómicos en contextos de alta incertidumbre estructural.

Palabras clave.

Crecimiento económico, Producto Interno Bruto, Ecuador, Modelos Arima, Box-Jenkins, Pronóstico Económico, Planificación macroeconómica.

1.- Introduction

Economic growth is one of the most relevant variables for

the analysis of the stability and development of countries,

since it reflects the productive capacity and structural

conditions of their economies, in this context, the Gross

Domestic Product (GDP) is the main indicator used to

measure economic activity, so its estimation and forecasting

are essential for the formulation of public policies.

decision-making in the business environment and the

evaluation of future scenarios. (Desiderio Noboa, 2022)

Technical University of Babahoyo; lzapata@utb.edu.ec; https://orcid.org/0009-0003-1497-2273 ; Babahoyo; Ecuador.

Bolivarian University Higher Institute of Technology; erhaymacana@itb.edu.ec; https://orcid.org/0000-0002-8708-3894; Guayaquil;

Ecuador.

University of Guayaquil; franscico.duquea@ug.edu.ec; https://orcid.org/0000-0001-9533-1635 ; Guayaquil; Ecuador.

Independent Researcher; genaro_cabezas@hotmail.com ; https://orcid.org/0000-0003-3595-3584; Hamilton, ON, Canada.

National University of Tumbes; rsanchez@untumbes.edu.pe ; https://orcid.org/0000-0003-3341-7382 ; Tumbes, Peru.

In the case of Ecuador, the evolution of GDP has been

marked by a notable dependence on oil exports,

vulnerability to external shocks and the implementation of

fiscal and monetary policies that have influenced its growth

dynamics, these factors have generated significant

variations in the expansion rates of the economy. which

makes it necessary to have robust statistical tools that allow

us to understand their historical behavior and project trends

with a greater degree of precision.(Asán Caballero, 2023)

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Chemical Engineering & Development

Journal of Science and Engineering

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Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 76

Within the methodologies of time series analysis, the Box-

Jenkins approach (ARIMA) has established itself as one of

the most used in the modeling and forecasting of economic

variables, its ability to identify stochastic patterns in data,

adjust parsimonious models and generate reliable

projections makes it a suitable alternative to study the

dynamics of GDP. In addition, its flexibility allows

capturing the non-stationary nature of economic series and

improving the quality of estimates over short-term

horizons.(Tudela-Mamani y otros, 2022)

In this framework, the present study aims to estimate and

forecast the GDP growth rate of Ecuador using the Box-

Jenkins methodology, in order to evaluate its predictive

capacity and provide empirical evidence that contributes to

the analysis of the national macroeconomic dynamics, thus

seeking to strengthen the academic debate and provide

useful inputs for the management and economic planning of

the country.(García Vázquez y otros, 2021)

The analysis of economic growth is a central issue in

economic research and in the formulation of public policies,

because the Gross Domestic Product (GDP) is the main

indicator that measures the productive capacity of a country.

In the case of Ecuador, the dynamics of GDP have been

subject to multiple internal and external factors, such as

dependence on oil exports, vulnerability to changes in

international commodity prices, the dollarization of the

economy, the fiscal and monetary policies applied, as well

as social and political phenomena that have generated

cycles of expansion and contraction in its growth.(de la

Oliva de Con & Molina Fernández, 2020)

This reality raises the need to have analytical tools that

allow us to understand the historical behavior of GDP and

anticipate its future evolution, however, a large part of the

studies on the Ecuadorian economy have focused on

descriptive analyses or aggregate macroeconomic

projections, which limits the ability to have rigorous and

validated statistical models for forecasting purposes.

In this context, the research problem arises: how to reliably

estimate and forecast Ecuador's GDP growth rate from its

historical series, using a statistical model that captures the

temporal dynamics of the data?

The Box-Jenkins methodology, using ARIMA models,

offers a robust approach to address this challenge, by

allowing to model the stochastic behavior of the series and

generate predictions with an adequate degree of precision

for decision-making, however, its application to the

Ecuadorian case still requires further exploration and

empirical validation, which justifies the present study.

The estimation and forecasting of the growth rate of the

Gross Domestic Product (GDP) of Ecuador, using the Box-

Jenkins methodology, is of great importance because it

combines economic analysis with statistical and

computational tools of engineering, this approach not only

contributes to the understanding of the national

macroeconomic dynamics, but also strengthens the capacity

of engineering to address complex problems in

environments of high uncertainty.(Duque-Aldaz y otros,

Identification of parameters in ordinary differential

equation systems using artificial neural networks, 2025)

In order to comply with the objective of this research, it is

proposed; as a first step, to be able to estimate and forecast

the growth rate of Ecuador's Gross Domestic Product (GDP)

through the use of statistical models, in order to generate

reliable information that supports economic planning and

strategic decision-making at the governmental, business and

academic levels. As a second step, it is proposed to analyze

the historical evolution of the GDP growth rate of Ecuador,

identifying trends, cycles and relevant patterns. As a third

step, it is proposed to select and apply appropriate statistical

and econometric models (for example: ARIMA, VAR, error

correction models) for the estimation and forecasting of

GDP. Finally, the results obtained will be compared with

the official projections (Central Bank of Ecuador, ECLAC,

IMF), evaluating similarities and discrepancies.(Castro

Rosales y otros, 2025)

1.1. Concept and relevance of the Gross Domestic

Product (GDP)

Gross Domestic Product (GDP) is a fundamental economic

indicator that represents the total monetary value of all final

goods and services produced within a country's borders

during a specific period, usually a year. Its theoretical origin

is mainly attributed to Simon Kuznets, who introduced it in

the 1930s to measure national economic activity, and it has

since established itself as the standard metric for assessing

the size and health of economies globally. GDP reflects both

tangible production, such as manufactured or agricultural

goods, and intangible services, such as education and

health, thus capturing the productive capacity and economic

dynamics of a country at any given time.(Cruz Ramírez y

otros, 2024)

In the context of Ecuador, GDP is especially relevant given

that the country has an economy highly dependent on

sectors such as oil exports, agro-industrial products and

natural resources. Sustained GDP growth is associated with

greater job creation, improved quality of life, and increased

general well-being of the population. Likewise, the analysis

of GDP and its evolution allows governments and public

entities to design and adjust economic, fiscal and social

policies, guiding investments in infrastructure, education

and health to promote a more balanced and sustainable

development within the national territory.(Núñez Ordóñez,

2023)

In addition to its usefulness in measuring aggregate output,

GDP functions as a key indicator of economic stability and

INQUIDE

Chemical Engineering & Development

Journal of Science and Engineering

Vol. 08 / Nº 01

e – ISSN: 3028-8533

ISSN – L: 3028-8533

Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 77

business confidence, influencing the perception of national

and international investors. The comparison of nominal and

real GDP allows us to identify real changes in production,

discounting inflationary effects. Also, its expression in per

capita terms makes it easier to evaluate the average level of

wealth and the economic progress of the population, an

aspect of particular importance for Ecuador due to the

existing regional and social inequalities. In this sense, GDP

not only measures economic volume, but also reflects the

structural conditions and challenges faced by the

Ecuadorian economy.(Duque-Aldaz & Pazan Gómez,

Factors affecting entrepreneurial intention of Senior

University Students, 2017)

1.2. Factors Affecting Economic Growth in Ecuador

Ecuador's economic growth is strongly influenced by both

internal and external factors that determine the dynamics of

the Gross Domestic Product (GDP). Among the external

factors, dependence on oil exports plays a central role, as

the national economy is highly linked to fluctuations in

international oil prices. Recent studies show that declines in

oil prices have a significant and more pronounced negative

impact on real GDP, also affecting tax revenues and public

spending, which are critical variables to sustain economic

growth. This sensitivity has highlighted the need to

diversify sources of income to reduce vulnerability to

external shocks arising from the volatility of international

markets.(Chérrez Sánchez y otros, 2025)

From a domestic point of view, the fiscal and monetary

policies implemented by the Ecuadorian government are

key mechanisms for influencing economic growth. Tax

collection, together with the management of public

spending, have a positive and significant relationship with

the evolution of GDP, since these resources allow financing

investments in infrastructure, education and other strategic

sectors. However, political stability seems to play a less

decisive role in economic variability than direct economic

variables, although social and political factors can generate

uncertainty that impacts business confidence and

macroeconomic expectations.(Sandoya Sánchez & Vásquez

Villon, 2004)

In addition, the Ecuadorian economy presents cycles of

expansion and contraction that are related to global

economic phenomena, such as the global financial crisis and

fluctuations in the oil market. Sectors such as mining,

agriculture and manufacturing play important roles in the

productive structure, although their contribution is

conditioned by international trends and internal dynamism.

Therefore, the interaction between external variables and

domestic economic policy decisions shapes the complex

dynamics of GDP growth in Ecuador, reaffirming the

importance of strategies aimed at strengthening resilience

and promoting sustainable and diversified economic

development.(Romero Ruiz y otros, 2024)

1.3. Models and methodologies for economic analysis

and forecasting

To analyze and forecast the evolution of the Gross Domestic

Product (GDP) in emerging economies such as Ecuador,

time series models have established themselves as

fundamental tools. These models allow us to capture the

dynamics and patterns intrinsic in historical economic data

to project their future behavior. Among the most widely

used are autoregressive models, moving averages and their

combinations, which adjust the temporal dependence of

economic variables. The ability of time series models to

handle sequential data and their flexibility to incorporate

seasonalities and trends makes them suitable for

environments with complex and noisy economic

data.(Morocho Choca y otros, 2024)(Herrera Mendoza,

2024)

The Box-Jenkins methodology, which includes the ARIMA

(AutoRegressive Integrated Moving Average) models, is

based on the systematic identification, estimation and

validation of the model that best fits the time series. This

methodology is especially valuable for economic estimation

and forecasting because it combines autoregressive and

moving average components after series differentiation to

achieve stationarity. Recent studies applied to the

Ecuadorian context have implemented ARIMA models to

forecast key variables, demonstrating the effectiveness of

the approach in capturing economic fluctuations and

generating predictions adjusted to real scenarios.(Sandoya

Sanchez & Abad Robalino, 2017)

However, ARIMA models and other traditional models

have both advantages and limitations. Among its strengths

is the relative structural simplicity and the ability to forecast

with historical univariate data. However, in contexts of high

economic volatility and external dependence, such as the

case of Ecuador, they may have difficulty anticipating

abrupt changes or incorporating the effects of exogenous

shocks, such as international crises or variations in

commodity prices, which affect GDP. For this reason, it is

recommended to complement these models with

multivariate approaches or current techniques that allow the

incorporation of external explanatory variables and better

capture the structural complexity of the economy.(Ochoa

González, 2024)

1.4. Statistical tests and criteria for model validation

In order to validate the suitability and accuracy of the

ARIMA models applied to the analysis of the Gross

Domestic Product (GDP), it is essential to perform

statistical tests to ensure the stationarity of the time series.

Among the most commonly used are the augmented

Dickey-Fuller (ADF) and Kwiatkowski-Phillips-Schmidt-

Shin (KPSS) tests. The ADF test contrasts the null

hypothesis that the series has a unit root —that is, it is not

stationary— against the stationarity alternative, and relies

on the inclusion of lagging terms to correct possible

autocorrelation. On the other hand, the KPSS test assumes

INQUIDE

Chemical Engineering & Development

Journal of Science and Engineering

Vol. 08 / Nº 01

e – ISSN: 3028-8533

ISSN – L: 3028-8533

Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 78

stationarity as a null hypothesis, evaluating whether the

series is the sum of a random walk and a stationary

component. The combination of both tests allows for a more

robust evaluation, since their null hypotheses are opposite,

providing greater certainty about the behavior of the

national GDP series.(Pincay Moran y otros, 2025)(Varas y

otros, 2023)

In addition, the analysis of correlogograms –

autocorrelation and partial autocorrelation functions – is

essential to identify seasonal patterns and temporal

dependencies in the data, facilitating the appropriate choice

of AR and MA parameters in ARIMA models. For the

optimal selection of the model, statistical information

criteria such as the Akaike Information Criterion (AIC) and

the Bayesian Information Criterion (BIC) are used, which

balance the fit of the model with its complexity, avoiding

overfitting. These criteria allow you to compare different

specifications and select the one that minimizes the

prediction error with the fewest parameters.(Li Ye & Paz y

Miño Robles, 2023)

Finally, residual diagnosis is a crucial step to validate the

quality of the estimated model, verifying that the residuals

are white noise, i.e., independent random variables with

zero mean and constant variance. This involves non-

autocorrelation tests – such as the Ljung-Box test – and

normality tests on the residuals, ensuring that the model has

correctly captured the relevant information in the series.

ARIMA models that successfully pass these statistical tests

provide reliable and robust estimates for GDP forecasting,

increasing the accuracy and usefulness of economic

analyses in the Ecuadorian context.(Arango Fuentes y otros,

2025)

1.5. Practical applications and complementary

approaches

Statistical models for the analysis and forecasting of the

Gross Domestic Product (GDP) in Ecuador have a

significant practical application in economic planning and

strategic decision-making. By using time-series models

such as ARIMA, policymakers and agencies can generate

reliable projections that guide the efficient allocation of

public and private resources, anticipating future scenarios.

This is essential to design fiscal policies, adjust budgets and

evaluate the impact of external and internal variables on the

national economy, allowing proactive management in the

face of changes in economic dynamics.(Macías Sandoval &

Tutiven Galvez, 2025)

To strengthen the predictive capacity and capture

interrelationships between multiple economic variables,

multivariate models such as Autoregressive Vector (VAR)

and Vector Error Correction Models (VECM) are used.

These models allow analyzing the co-integration and

dynamic relationships between various macroeconomic

variables, including inflation, exchange rates, interest rates,

and exports, enriching the understanding of the causes and

effects on GDP variation. Its use complements and expands

the information provided by univariate models, adapting

better to complex and highly interrelated economic contexts

such as the Ecuadorian one.(Cruz Peña, 2024)

Recently, there has also been an increase in the

incorporation of hybrid methods that combine traditional

statistical models with machine learning and artificial

intelligence techniques to improve the accuracy of

economic forecasting. These techniques make it possible to

take advantage of large volumes of data and detect non-

linear patterns that escape conventional approaches,

increasing robustness in contexts of high volatility and

external dependence. In Ecuador, the integration of these

approaches represents a key methodological advance to

address the limitations inherent in classical models and

empower decision-making based on more accurate and

adaptive predictive analytics.(Fu-López y otros,

2025)(Lliguizaca Dávila y otros, 2020)

2.- Materials and methods.

The methodology used in this research is described below:

Facts:

Annual historical series of Ecuador's GDP (1965–2023)

provided by the Central Bank of Ecuador (BCE).

Software and analytical tools:

EViews 12 (x64) for time series analysis and ARIMA model

estimation.

Experimental design

Type of study: quantitative, longitudinal, based on time

series.

Variables studied:

Dependent: GDP growth rate.

Method validation:

Stationarity tests (ADF, KPSS) were applied to ensure the

suitability of the time series models.

Information criteria (AIC, BIC) were used to select the most

appropriate models.

The results were compared with official forecasts from the

ECB and ECLAC to assess consistency.

Procedures

Data collection:

Download historical GDP series and related

macroeconomic variables from the ECB, ECLAC and

INEC.

Debugging and preparation:

Data cleansing, outlier removal, and homogenization of

units and periods.

Exploratory analysis:

Descriptive statistics and visualization of trends, seasonality

and economic cycles.

Modeling:

Application of ARIMA models for individual series.

Model validation and tuning:

Residual, autocorrelation and heteroskedasticity tests.

Comparison with official forecasts and adjustment of

parameters according to results.

Forecast generation:

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Chemical Engineering & Development

Journal of Science and Engineering

Vol. 08 / Nº 01

e – ISSN: 3028-8533

ISSN – L: 3028-8533

Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 79

Annual GDP projection for the next four years (2024–

2027).

Presentation of results:

Charts and graphs in EViews, including optimistic,

pessimistic, and expected growth scenarios.

Data analysis

Descriptive statistics: means, standard deviations, trends

and seasonality.

Time series models: ARIMA, SARIMA for individual

estimates.

Model Validation:

Unit root test (ADF, KPSS).

Autocorrelation analysis (ACF, PACF).

Information criteria (AIC, BIC).

Forecasts: 95% confidence intervals and comparison with

historical series.

3.- Analysis and Interpretation of Results.

3.1.- Presentation of results:

Phase 1 Identification

Table 1. Historical Series of the Gross Domestic Product (GDP) of Ecuador

(1965-2023)

Source: Central Bank of Ecuador.

Evolution of GDP in Ecuador (1965-2023)

Figure 1.- Evolution of GDP in Ecuador (1965-2023)

According to the graph, the series does not show stationarity

in the mean, although it does show a trend, therefore, we

will proceed to check this assumption, then we will check

the assumption.

Table 2. Results of the Unit Root Test (ADF Test)

Augmented Dickey-Fuller Test

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Chemical Engineering & Development

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Guayaquil – Ecuador

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Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 80

A time series is non-stationary in mean when its expected

value (the mean) is not constant and changes over time.

We observe that the p-value indicates that the series is non-

stationary on average, therefore, it is necessary to apply

transformations, such as differentiation, to make it

stationary.

The following are the hypotheses of the test:

Ho (null): the series has a unit root → is not stationary.

H1 (alternative): the series has no unit root → is stationary.

P-value (0.9735), is very high, much higher than any typical

significance level (0.01, 0.05, 0.1), this does not allow Ho

to be rejected, which means that the series is not stationary.

First GDP difference

Table 3. GDP (Gross Domestic Product) - First Difference

First Difference in GDP

Figure 2.- First Difference in GDP

Then we see that the graph no longer has a trend and

apparently the average is around 0, we do the Augmented

Dickey-Fuller Test (ADF Test).

Table 4. Unit Root Test (DAF) Results on the First GDP

Difference

The new variable Dpbi has been subjected to a stationarity

analysis, which confirmed that it is stationary.

Subsequently, the correlogram is performed.

H0 (null): the series has a unit root → is not stationary.

H1 (alternative): the series has no unit root → is stationary.

It is much lower than any typical significance level (0.01,

0.05, 0.1), this means that we reject the null hypothesis Ho.

Then we perform the correlograme.

Table 5. Correlogram of the First Difference in GDP

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Guayaquil – Ecuador

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Pag. 81

Phase 1: Identification

Partial Correlation AR:(1)

Autocorrelaction MA:(1)

Phase 2: We choose a model

d(PBI) c ar(1)

Table 6. Results of the Estimation of the Model 1 d(gdp) c

ar(1)

Table 7. Results of the ARMA Estimation by Maximum

Likelihood (OPG - BHHH) d(pbi) c ar(1)

The results of the ARIMA model estimation show that all

coefficients are statistically significant at a 95% confidence

level, this is concluded by observing that their p-values are

less than 0.05.

C (Constant): The p-value of 0.0104 is less than 0.05,

indicating that the model constant is significant. This

suggests that there is a non-zero mean in the series after

differentiation.

AR(1) (Autoregressive Term): With a p-value of 0.0025,

this coefficient is highly significant, this confirms that the

current value of the series is strongly correlated with its

value in the previous period (a lag).

SIGMASQ (Variance of Error): The p-value of 0.0000 is

extremely low, which means that the variance of the model

residuals is statistically significant. This is a good indication

that the model is correctly capturing the structure of the

series, and that the variance of the errors is not zero.

Proposed model

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

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{Ho: 0

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{: ≠0 significant because the p-value is 0.0001

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So phase 2 does comply because the values of the

coefficients are significant.

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Guayaquil – Ecuador

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Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 82

P-Value:

If p < 0.05 → you reject H₀

If p ≥ 0.05 → you don't reject H₀

Phase 3: Diagnosis

It is a function of the normality of errors and

Autocorrelation of errors.

View

Residual Diagnostic

Histogram – Normality Test

Histogram of the residues

Figure 3.- Histogram of the residuals

**In this graph we see that errors tend to be normal with

mean 0 and variance 1.

The Jarque-Bera probability is 0.000251 therefore the

distribution of errors is Not Normal.

So we go back to Phase 1.

Then equation d(gbi) c ar(1) ma(1)

Table 7. Results of the Estimation of the Model 2 d(gdp) c

ar(1) ma(1)

Table 8. Results of the ARMA Estimation by Maximum

Likelihood (OPG - BHHH) d(pbi) c ar(1) ma(1)

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Journal of Science and Engineering

Vol. 08 / Nº 01

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Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 83

{Ho: φ_0=0

{H_1: φ_0≠0 significant because the p-value is 0.0001

So phase 2 does comply because the values of the

coefficients are significant.

P-Value:

If p < 0.05 → you reject H₀

If p ≥ 0.05 → you don't reject H₀

Phase 3: Diagnosis

It is a function of the normality of errors and

Autocorrelation of errors.

View

Residual Diagnostic

Histogram – Normality Test

Graph 4: Histogram of the residues

Figure 4.- Histogram of the residuals

**In this graph we see that errors tend to be normal with

mean 0 and variance 1.

The Jarque-Bera probability is 0.000166 therefore the

distribution of errors is Not Normal.

So we go back to Phase 1.

Then equation d(gbi) c ar(1) ma(1)

We then check for autocorrelation

View

Residual Diagnostic

Correlogram-Q-Statistics

Table 9. Map of the d(gdp) model c ar(1) ma(1)

Looking at the probabilities of errors are not self-correlated.

Phase 4. Prognosis

2024-2027

Ecuador's GDP forecast for the period 2024-2028 (ARMA

Model)

Figure 5. Ecuador's GDP forecast for the period 2024-2028

(ARMA Model)

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Chemical Engineering & Development

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Vol. 08 / Nº 01

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ISSN – L: 3028-8533

Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 84

Table 11. Ecuador's Gross Domestic Product (GDP):

Historical and Forecasted Values

GDP Trend and Forecast

Figure 6.-GDP Trend and Forecast

3.2.- Analysis of results:

The study showed that Ecuador's GDP series was not

stationary at its original level, which required the

application of the first difference to stabilize the average.

The identified ARIMA model integrated autoregressive and

moving average components, whose coefficients were

statistically significant, confirming the validity of the

adjustment. The residuals did not show autocorrelation,

which reinforced the adequacy of the model. The forecast

for the period 2024–2027 indicated a moderate growth

trend, with alternative scenarios that contemplated

optimistic and pessimistic variations. These results were

consistent with the official estimates issued by national and

international organizations, which strengthened the

reliability of the analysis carried out.

3.3.- Interpretation of results:

The findings confirmed the usefulness of the Box-Jenkins

methodology in predicting Ecuadorian GDP, allowing the

temporal dynamics of the economy to be captured in the

short term. The projected performance reflected a gradual

recovery after recent external shocks, particularly those

resulting from the pandemic and oil price volatility. The

consistency with the official projections showed that the

model can serve as a complement to the economic

forecasting systems already implemented, likewise, it was

shown that the use of time series contributes to

strengthening economic planning, by offering robust

estimates in contexts of uncertainty.

4.- Discussion.

The study was based exclusively on historical GDP series,

which limited the incorporation of additional structural

factors, such as investment, consumption or non-oil exports.

The application of ARIMA models, although adequate to

capture temporal patterns, did not allow to explain

underlying economic causalities. In addition, the non-

normality of the residuals in certain models represented a

methodological restriction. Finally, the analysis focused on

the short term, which reduced its applicability to medium

and long-term horizons.

It is recommended to complement future studies with

multivariate models, such as VAR or VECM, which allow

the inclusion of additional macroeconomic variables to

improve explanatory capacity. In the same way, it would be

pertinent to integrate hybrid approaches that combine time

series techniques with machine learning methods, in order

to increase accuracy in high volatility scenarios. clear and

technical language, avoiding ambiguities. It is suggested to

extend the projection horizon to assess the sustainability of

growth in the medium term. For all these reasons, it is

recommended to compare the results with sectoral

indicators to offer a more comprehensive view of the

national economic dynamics.

INQUIDE

Chemical Engineering & Development

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Vol. 08 / Nº 01

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Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 85

The results obtained reflected that the Ecuadorian GDP

series presented a non-stationary behavior at its original

level, which coincided with the dynamic and volatile nature

of emerging economies. The application of the first

difference allowed stabilizing the series and obtaining an

ARIMA model with statistically significant parameters,

which confirmed the methodological validity of the Box-

Jenkins approach in the analysis of macroeconomic

variables. From the theoretical framework, the results

ratified the usefulness of time series models in the capture

of stochastic patterns, as established by Box and Jenkins in

their methodological proposal. The consistency with the

official estimates of the Central Bank of Ecuador and

ECLAC reinforces the relevance of the model applied,

demonstrating that, even in contexts of uncertainty, the

methodology used constitutes a robust tool for economic

analysis.

In the context of the study, projections indicated moderate

GDP growth for the period 2024–2027, suggesting a

scenario of gradual recovery after recent external shocks.

These findings are directly related to the proposed objective

of estimating and forecasting the rate of economic growth

in the short term, generating reliable information that

supports planning and strategic decision-making.

5.- Conclusions.

The study showed that Ecuador's GDP series was not

stationary at its original level, so it required differentiation

for its analysis. The identified ARIMA model presented

statistically significant coefficients and residuals without

autocorrelation, validating its suitability for estimation. The

forecasts obtained projected moderate growth of the

economy between 2024 and 2027, in accordance with

optimistic and pessimistic scenarios, and in line with the

official estimates of national and international

organizations.

The research provided empirical evidence that confirms the

usefulness of the Box-Jenkins methodology in the

prediction of macroeconomic variables in contexts of

uncertainty. A robust statistical model was offered that

complements existing economic forecasting systems,

constituting a practical tool for macroeconomic planning

and management. In addition, the study strengthened the

link between the theoretical analysis of time series and its

application in the Ecuadorian economy, contributing both to

the academic field and to decision-making in public policies

and business strategies.

In the practical field, the results obtained offer a support tool

for economic planning and strategic decision-making in the

public and private sectors. Short-term projections of GDP

make it possible to anticipate growth scenarios, which

facilitates the design of more effective fiscal and monetary

policies, as well as the preparation of business plans

adjusted to the macroeconomic situation.

On the theoretical level, the study reaffirms the relevance of

Box-Jenkins models for the analysis of time series applied

to emerging economies, demonstrating their ability to

capture stochastic patterns and generate reliable forecasts.

The research also contributes to the economic literature by

validating a specific model for Ecuador, strengthening the

evidence on the applicability of advanced econometric

methodologies in contexts characterized by high volatility

and dependence on external factors.

It is suggested that the time horizon of the projections be

extended in order to assess the sustainability of economic

growth in the medium and long term. It is also pertinent to

incorporate additional macroeconomic variables – such as

investment, consumption, non-oil exports and public

spending – to enrich the models and improve their

explanatory capacity.

Future studies could explore multivariate approaches, such

as VAR or VECM, as well as hybrid models that combine

time series techniques with machine learning algorithms,

which would increase the accuracy of forecasts in high-

volatility scenarios. It is also recommended to make

comparisons with structural models to analyze not only the

temporal dynamics of GDP, but also the causal relationships

between the main determinants of economic growth.

Finally, the need to evaluate the results at the sectoral level

is raised, with the purpose of identifying specific patterns in

key productive branches and strengthening economic

planning from a more comprehensive perspective.

6.- Contributions of the authors (Taxonomy of

contributors' roles - CRediT)

1. Conceptualization: Leonor Alejandrina Zapata

Aspiazu, Edwin Haymacaña Moreno.

2. Data curation: Leonor Alejandrina Zapata Aspiazu.

3. Formal analysis: Leonor Alejandrina Zapata Aspiazu,

Edwin Haymacaña Moreno.

4. Acquisition of funds: N/A.

5. Research: Leonor Alejandrina Zapata Aspiazu, Edwin

Haymacaña Moreno.

6. Methodology: Francisco Javier Duque-Aldaz, Raúl

Alfredo Sánchez Ancajima.

7. Project management: Francisco Javier Duque-Aldaz,

Raúl Alfredo Sánchez Ancajima.

8. Resources: Leonor Alejandrina Zapata Aspiazu,

Francisco Javier Duque-Aldaz.

9. Software: Leonor Alejandrina Zapata Aspiazu, Edwin

Haymacaña Moreno.

10. Supervision: Félix Genaro Cabezas García, Raúl

Alfredo Sánchez Ancajima.

11. Validation: Félix Genaro Cabezas García.

12. Visualization: Edwin Haymacaña Moreno.

13. Writing - original draft: Leonor Alejandrina Zapata

Aspiazu, Francisco Javier Duque-Aldaz.

INQUIDE

Chemical Engineering & Development

Journal of Science and Engineering

Vol. 08 / Nº 01

e – ISSN: 3028-8533

ISSN – L: 3028-8533

Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 86

14. Writing - revision and editing: Francisco Javier Duque-

Aldaz, Félix Genaro Cabezas García, Raúl Alfredo

Sánchez Ancajima.

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Chemical Engineering & Development

University of Guayaquil | Faculty of Chemical Engineering

Guayaquil – Ecuador

https://revistas.ug.edu.ec/index.php/iqd

Email: inquide@ug.edu.ec

francisco.duquea@ug.edu.ec

Pag. 87

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