Introduction

At the beginning of the 19th century, David Ricardo (1950/1993)specified the participation of economies in the international context and the benefits through their specialization in those goods that present comparative advantages, which in the Ecuadorian context is beneficial due to thegeographic location for flower production (Moreno et al., 2016); therefore, an economy with a favorable trade balance helps economic growth (Zack & Dalle, 2015, as cited in Aguilar et al., 2020). Consequently, it is important to analyze exports, because according to Gladys Mireya Valero Córdoba et al. (2016), they represent the capacity of an economy to produce goods that will cross national borders to satisfy the needs of international economies and are related to what José Elías Durán Lima and Mariano Álvarez (2008) consider exports are the sales of goods and services by residents of one economy to others from another economy and thatthey are equivalent to the production not consumed in the country.

Ecuador, in particular, has great natural resources such as bananas, cocoa, shrimp, flowers, etc., and some of them have experienced important booms¹ throughout the country's agroeconomic history (Cedillo Villavicencio et al., 2021). However, these goods are seasonal and respond to certain characteristics of the national and international market for their commercialization.

To model and forecast the behavior of a variable such as exports, there are several methodologies, each one being more rigorous than the other and crucial for econometric analysis. In this particular case, the one based on the historical behavior of the export variable was chosen, its level of volatility and its period of seasonality, using Generalized AutoRegressive Conditional Heteroscedasticity (GARCH), which is part of the family of ARCH models that use maximum likelihood estimation of parameters (Espinosa Acuña & Vaca González, 2017).

The seasonality condition allows identifying certain patterns that are repetitive for some variables such as exports (X) of natural flowers, toy sales, seasonal illnesses due to climate changes, etc. The flowers of Ecuador are among the best in the world. Their characteristics are mainly: thick stems and large extension, large buds and bright colors. In addition, the great distinguishing feature of the Ecuadorian rose is its long vase life after cutting (Subgerencia de Análisis e Información, 2017). Among the varieties are: Gypsophila, carnation, roses, lilies, and others. According to the National Institute of Statistics and Census, according to the International Standard Industrial Classification, flowers fall under code A0119.03 “Growing of flowers” ¿, including the production of cut flowers and flower buds (Instituto Nacional de Estadísticas y Censos [INEC], 2012). This classification is used by the Central Bank of Ecuador to prepare the statistics used in this research (Banco Central del Ecuador [BCE], n.d.).

According to the National Finance Corporation, in 2017 there were 204 companies whose economic activity was the cultivation of flowers, located mostly in Pichincha with 77%. In 2018, of the 208 companies, 74% were also located in this same province. In 2019, of the 181 companies registered with the Superintendence of Companies, 74% remained in Pichincha, and according to 2020, of the 237 companies, 73% continued their economic activity in Pichincha, followed by Cotopaxi as the most representative (Subgerencia de Análisis e Información, 2017). The industrialization process of this sector demands important sources of economic resources and, as we have seen, there is a high concentration of companies in the highlands due to the high (Henao et al., 2022) of companies in the highlands due to climatic conditions and irrigation water (Mena Vásconez et al., 2017). Table 1 below shows the classification of the companies dedicated to this activity:

Table 1

Classification of companies by size in Ecuador

Source: Subgerencia de Análisis e Información (2018), Subgerencia de Análisis de Productos y Servicios (2019, 2020, 2021). Prepared by: Authors

As shown in Table 2, in the last four years, the highest number of employees was recorded in year 2018 with 33,494 people employed in the flower sector, followed by 29,867 in 2017, 28,775 in 2020, and 25,177 in 2019.

Table 2

Classification of companies by number of employees

Source: Subgerencia de Análisis e Información (2018), Subgerencia de Análisis de Productos y Servicios (2019, 2020, 2021) .

With respect to production and harvested area, their evolution over the last five years can be seen in Illustration 1 below, taking into account that the rose is the most sold species in the local and international market.

Illustration 1

Source: Subgerencia de Análisis e Información (2018), Subgerencia de Análisis de Productos y Servicios (2019, 2020, 2021)

Flowers are a non-traditional export product for Ecuador², whose figures for the last 13 years, including the current year 2022, are shown in Illustration 2, which highlights that in 2021 they grew by 12% compared to 2020, when flower exports fell to $827,142.1 as a result of the decrease in demand for many exportable products due to the effects of the COVID-19 pandemic³.

Illustration 2

Export of Ecuadorian natural flowers

Source: BCE: annual statistics. Prepared by: Authors

The main destinations of Ecuadorian exports in 2021 were: United States with 37%, Russia with 14%, Holland with 10%, Ukraine and Italy with 3%, Canada with 4% and the rest of the world with 29%, (Subgerencia de Análisis de Productos y Servicios, 2021) therefore, the trade balance for this product is favorable, including the year 2020, which was $827 thousand dollars FOB due to the limited import of flowers from the world. With respect to imports (M) to the year 2019 there was a highly significant value in its historical evolution, reaching $255,036.85 FOB imports, being the countries of Colombia with 99% and China with 1% respectively the countries of origin to the years 2020 and 2021. The financing received by this sector comes in 93% from Private Banks and 7% from the Public; the latter, through the National Finance Corporation mostly in the province of Pichincha with 56%, followed by Cotopaxi, Imbabura, Carchi and Cañar with 16%, 14%, 8% and 6% respectively between 2018 and 2021 (Subgerencia de Análisis de Productos y Servicios, 2021).

Finally, the article is structured as follows: a section with an introduction on the importance of the analysis of the Ecuadorian export sector, the next section contains the GARCH methodology applied to the historical series extracted from the Central Bank of Ecuador. Also; in the results section the calculated seasonal model and the stationarity tests are shown, in the discussion section some studies related to the floriculture sector and finally the section on conclusions and recommendations for future research related to the prediction of economic variables.

Justification

It is important for students, teachers and the scientific community to analyze the behavior of a seasonal economic variable such as exports of Ecuadorian natural flowers, since it allows us to study, analyze and understand its cyclical component related to international demand, especially in the months of February and May of each year while in the rest of the months exports fluctuate, an essential condition of the GARCH volatility models, which at a macroeconomic level allow the construction of scenarios based on public policies of incentives or benefits for economic sectors that boost the economy between them the agricultural one.

The practical application of this type of models is reflected in several disciplines; for example, Olga Formigoni Carvalho Walter et al. (2013) analyzed the influence of prices on motorcycle sales using a SARIMA forecast model (1,0,1) (2,1,0)₁₂. On the other hand, Juan Tudela Mamani et al. (2022) studied the demand for tourists to Peru, through a seasonal ARIMA model, with characteristics (1,1,1) (0,1,1)₁₂ that captured the cyclical essence of tourism for decision making as well as that Thushara et al. (2019) who agreed that tourism in Sri Lanka has grown, generating foreign exchange and employment, the prediction of which was possible through the use of a SARIMA model (3,1,3) (2,1,2)₁₂. For their part, Wanderson de Paula Pinto et al. (2015), in their study on the flow of the Doce River and its seasonal behavior, obtained a SARIMA model (1,1,1) (1,1,2)₁₂ for the management of the Municipality of Colatina in the prevention of possible natural disasters. Regarding the application in the agricultural sector of Submedio the Valley of São Francisco River in Brazil, on the export of mango, the price of this fruit could be related through a SARIMA model (4,1,1) (0, 1,3)₂ of biannual seasonality for the determination of public policies related to subsidies to producers (Lima et al., 2013). Concerning the environment, Claudionor Ribeiro da Silva et al. (2018), carried out a study on the recovery forecasts of Caatinga and vegetation areas in the Serra das Capivaras National Park in the state of Piauí - Brazil for the conservation of the biome and determined a SARIMA model (1,2,2) (0,1,2)₁₂ for making decisions aimed at protecting natural areas.

In this sense, there are international studies analyzing the statistical behavior of this variable. However, the econometric background in Ecuador related to the use of the GARCH methodology is limited and not necessarily oriented to the flower sector, which highlights the importance of this research.

Objective

To build an econometric model of the seasonal behavior of Ecuadorian natural flower exports to the international market using the GARCH methodology to predict economic scenarios that can inform public and private decision-making related to foreign policy.

Methodology

The research was descriptive and used a mixed approach, where the quantitative analysis was based on the Box - Jenkins (1970) methodology better known as ARIMA (Pérez Cargua, 2017) by studying a seasonal factor that allowed understanding this effect in the longitudinal monthly historical series, corresponding to 259 observations from January 2001 to July 2022, obtained from the (BCE, n.d.) in statistical-documentary form through the econometric program Eviews 9. The application of this methodology began with the specification, verification, prediction, and use of the model Altamirano, 2021, which started with the review of the original model through the application of stationarity tests to ensure that the series was stable and allowed capturing the seasonal component for prediction. When this condition was not met, a first-difference transformation was applied to the series of natural flower exports to subsequently obtain a robust SARIMA model of monthly frequency (f=12) which served as the basis for the GARCH⁴ model (1,1) (Javed et al., 2022) model, which was subjected to validation tests for use in forecasting five data points between August and December 2022.

Results

By generalizing the ARMA (p,q) model by incorporating a difference to make the process stationary it becomes ARIMA (p,d,q) to eliminate the unit root. It is important to consider that the three components of this model are: autoregressive, integration by difference, and moving averages (Fernández Jiménez, 2008; Gujarati & Porter, 2010; León Anaya, 2017). The ARIMA equation is as follows:

[1]

By adding seasonality conditions to the ARIMA model, two important extensions are derived, which are: SAR and SMA, which relate to seasonal autoregressive and moving average processes that together make up the SARIMA model (P,D,Q), where D is the integration process or seasonal difference (Rosales Alvarez et al., 2010). This model allows the variable Yt to correlate with its seasonal lags (Franses et al., 2014).

The seasonal autoregressive variant of the SAR (p,d,q) (P,D,Q)f equation:

[2]

The seasonal moving average variant of the SMA (p,d,q) (P,D,Q)f equation:

[3]

The SAR and SAM combination in SARMA would be:

[4]

The SARIMA combination (p,d,q) (P,D,Q)f:

[5]

The Garch (p,q) model is mathematically defined as follows (El Jebari & Hakmaoui, 2019) as follows:

[6]

The GARCH model (generalized autoregressive conditional heteroscedastic conditional model) uses the variance and its lags ($u_{t-i}^2$) where $\beta$ is the volatility factor and $\alpha$ the shocks that affect the model and it is required that:

[7]

When analyzing the original series in Illustration 3 (a), it is possible to observe values that exceed the average values and indicate seasonal characteristics that are repeated each period of the historical series under study.

Illustration 3

Seasonal Chart of Ecuadorian Flowers

Prepared by: Authors

By obtaining a graph in Eviews that breaks down the seasonality of the export series, it is possible to observe monthly periods that experience high FOB values, such as February, March, and May throughout the entire statistical series; and, in the case of Ecuador, it corresponds to events such as Valentine's Day as well as Mother's Day, when sales experience their highest economic growth internationally, and that according to Reinoso (2016, as cited in Cedillo Villavicencio et al., 2021), there are periods of high demand at high prices as well as low demand for the product, generating low export values to the Ecuadorian economy as is shown in Illustration 3 (b).

The ARIMA methodology begins with the specification, i.e. the evaluation of the natural flower export series and the contrasts that were applied: Dickey Fuller Augmented (DFA), Phillips Perron (PP), Kiatkowski, Phillips, Schmidt and Shin (KPSS) and Elliott Rotheberg and Stock (ERS) (Altamirano, 2021).The results are presented in Table 3 below.

Table 3

Contrasts to determine the stationarity of the flower export series⁵.

Source: Altamirano (2021) . Prepared by: Authors

As can be seen, the series is not stationary; therefore, it requires a transformation process through a first difference to allowthe mean to be zero, E(wt )=0, and the variance approximately constant, Var(wt )=σ², a process known as white noise (Hamilton, 1994; Morales Oñate, n.d.). We therefore proceed to evaluate the criteria again in Table 4.

Table 4

Contrasts to determine the stationarity of the Differentiated Flower Export Series

Source: Altamirano (2021). Prepared by: Authors

With these data, we proceed to determine the appropriate model and verify it according to the Box-Jenkins methodology, as shown in Table 5 below.

Table 5

Significance of the coefficients of the proposed models

Prepared by: AuthorsNote: Coefficients in color are significant to 95%

As can be seen, 11 models were obtained, and we proceeded to verify the one whose coefficients are significant, as in the case of models 1, 5, 6, 7, and 10, whose probability (p < 0.05. Through the application of the validation criteria Akaike (AIC), Schwarz (BIC), and Hannan-Quinn (HQ), the one with the smallest coefficient was chosen as technically adequate (Sánchez Verdezoto, 2021), as can be seen in the records of Table 6.

Table 6

Validation Criteria for the models

Prepared by: Authors

According to the evaluation shown in Table 6, the model that technically fits best is model 10. While, under the parsimony criterion, the first models could be considered, they would not capture the essence of the seasonality that is intended to be demonstrated in this research.

Model 10: d_ord_export c ar(2) ma(1) sar(12) sma(12)

The model was subjected to unit root analysis, in order to rule out the possibility that the model is unpredictable and can be reliable, as shown in Illustration 4 (a) below:

Illustration 4

Prepared by: Authors

In this sense, the model does not contain unit roots and the analysis of the residuals through the Durbin-Watson Criterion allows for the analysis of their independence, as shown in Illustration 4 (b) (Altamirano, 2021). The Durbin-Watson criterion is used to determine the independence of the residuals (Talero Sarmiento et al., 2019):

[8]

The DW coefficient of 1.925606 allows us to accept the null hypothesis of independence of the residuals (Altamirano Pérez et al., 2022). With respect to the analysis of the squared residuals we observe that the model suffers from heteroscedasticity, since the probability values are less than 0.05, and the null hypothesis of homoscedasticity is rejected (see Illustration 5 (a)).

Illustration 5

Prepared by: Authors

The probability value is less than 0.05 (p<0.05) and indicates a volatile model, which is complemented by the heteroskedasticity test in Illustration 5 (b) with a p-value of 0.0000, which determines variance problems.

To correct the variance, it has been proposed that the model be structured under the ARCH family of heteroskedastic models developed in 1982⁶ and its variant or extension GARCH (generalized autoregressive conditional heteroskedastic model) (El Jebari & Hakmaoui, 2019), proposed by Bollerslev (1986). This model abandons the traditional assumption of normality for the presence of time-varying variance (Javed et al., 2022) to correct these problems that affect the predictive process and is based on maximum likelihood criteria. The results of the GARCH model are shown in Illustration 6:

Illustration 6

Prepared by: Authors

By analyzing the unit root processes, residuals and squared residuals to detect autocorrelation and heteroscedasticity, the problem has been corrected obtaining an acceptable coefficient of determination of 76%.

Illustration 7

Prepared by: Authors

The probability p-values in Illustration 7 (a), exceed the condition of 0.05, therefore, there is independence of the residuals. In Illustration 7 (b), the p-values similarly exceed 0.05, which certifies the stability of the model, and especially when it is complemented with the Heteroscedasticity Test, which produced the values shown in Illustration 8, These values exceed the 0.05 threshold, as shown below:

Illustration 8

Prepared by: Authors

The next stage correlates with the prediction according to the proposed ARIMA methodology. Therefore, we proceed to determine the predictability criteria in Illustration 9 (a) for model 10, the results of which are presented below:

Illustration 9

Prepared by: Authors

The criteria that determine the model's reliability are analyzed; its mean absolute percentage error (MAPE) is 10%, which means that it can be used within a moderate range for forecasting, considering the high volatility that can occur in the international market due to different circumstances that affect exports of various Ecuadorian products, as has happened with the pandemic and the current Russian invasion of Ukraine. Illustration 9 (b) shows the results obtained from the technical proposal of using the GARCH model with the SARIMA model as a fundamental basis for the original data.

The predictions for the next five months, from August to December 2022 using this model are shown in Illustration 10 (a) in graphical form:

Illustration 10

Graph of the Projection of Ecuadorian Exports

Prepared by: Authors

The projection equation that allows the modelling of this macroeconomic series of exports is detailed below:

The model corresponds to a SARIMA (2,1,1) (1,0,1)₁₂, where the coefficient ar(1) remains muted in the model. The projected values for the five out-of-sample data are broken down graphically and numerically in Illustration 10 (b), These projections allow for good growth expectations that will help sustain the national economy by providing resources to support decision-making related to the use of foreign currency in the General State Budget (PGE).

Discussion

The application of the SARIMA model is broad, in this case applied to the prediction of exports of Ecuadorian natural flowers, where the SARIMA model (2,1,1) (1,0,1)₁₂ indicates that with a moderate MAPE of 10% meets the conditions of stationarity and can be used to predict the last months of the year 2022. On the other hand, in the investigation of Carlos Andrés Salazar Bernal (2020) about the relationship of non-traditional exports of Ecuadorian flowers with respect to the economic growth, it is proposed a direct correlation model using ordinary least squares (OLS), obtaining a coefficient of determination of 0.93 to complement his study. Likewise, Josselin Gabriela Heredia Landeta (2023) conducts an analysis of the comparative advantage that Ecuadorian flowers had in the international market in the year 2021. This analysis is presented through multiple linear regression, obtaining a significant correlation of 77.3%; however, this analysis shows that flower production is inversely related to competitiveness. Regarding, Mayorga Abril et al. (2022) concur with the previous authors and propose four types of econometric models using ordinary least squares (OLS) to measure the competitiveness of Ecuadorian flowers compared to Colombian ones; exported to) the United States, concluding that in the period 2005 - 2020, Ecuador's competitiveness decreased by 56.9%, despite the growth in figures reported by the Central Bank of Ecuador and the statistics projected in this investigation.

Álvaro Román Bayona García y Lady Liliana Morales Choez (2019) considered two types of models for the analysis of exports of canned fish and flowers: a linear probability model (MPL) and a Probit-Logit model, and identified variables that affect these exports, including the size of the company, modernization, foreign investment, seniority, and properties; allowing the identification of public incentive policies that benefit these sectors.

Conclusions

There is evidence that Ecuadorian flower exports are subject to important seasonal influences that affect the economy. This implies that there are periods with higher and lower demand for flowers, related to holidays and special events in importing countries. This non-traditional product could be modeled using the Box-Jenkins methodology, obtaining a SARIMA model (2,1,1) (1,0,1)₁₂, which, after its evaluation, was suitable for building a GARCH model using maximum likelihood techniques that allowed capturing the volatile and cyclical characteristics of the monthly time series.

The contribution of GARCH models to governments is essential because they can directly predict and better manage risks associated with these variables and foreign policy strategies, which directly impacts economic policy decision-making that must consider the influence of external factors such as weather, price fluctuations as well as policies and trade agreements with other countries.

Finally, the use of the GARCH methodology in time series analysis has proven to be an effective tool in government economic policy and in making decisions about incentive policies associated with seasonal variables of SARIMA models because it can accurately identify and model the volatility of economic data and help governments make more efficient decisions.

Recommendations

The use of this methodology allowed the construction of models that were evaluated until the optimal one was obtained. Nevertheless, it is recommended for future research that the historical series be expanded and updated with more data so that the average absolute error percentage decreases and a model with a higher degree of robustness can be obtained.

Additionally, it is recommended that economic variables such as inflation, commodity prices, and imports, among others that contain high fluctuations, be understood and technically analyzed by the government's economic team, especially during periods of high demand, when the government could implement expansionary policies to control, facilitate, and promote flower exports, such as reducing red tape, improving logistics infrastructure, and incentivizing farmers to invest. In contrast, during periods of low demand, the government could take measures to counteract the effects of the crisis on the economy, diversifying productive investment towards other agro-export sectors and promoting, for instance, tourism as a factor of economic growth.

Limitations

The proposed methodology could be stronger if complemented with prediction techniques such as neural networks, multiple regression models, VAR models, among others that enrich the theoretical-practical scaffolding of applied econometrics.

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Información adicional

Clasificación JEL: M11, Q53